The role and significance of reflexive games. Reflexive business games. H. Reflective stage

To use the preview, create an account for yourself ( account) Google and sign in: https://accounts.google.com

Preview:

Final report on the work done on the implementation of the "Reflexive circle" plan in the framework of socialization

Reflection is a person's reflection aimed at analyzing himself (self-analysis) - his own states, his actions and past events.(PHOTOGRAPHY FROM SPACE)

"Reflexive circle" is a technology that allows you to develop the speech of preschoolers, the thoughts of children. The circle contributes to the improvement of speech as a means of communication, helps children make assumptions, draw the simplest conclusions.

On daily reflective circles in groups preschool age The teacher asks questions, which the children actively answer.

(A PHOTO)

During the daily reflective circles throughout the year, the children learned to listen carefully to the teacher and their peers, not to interrupt each other.

(A PHOTO)

Children have learned to use the rules that are shown in the pictograms and are in each group at the level of the children's eyes.

(PHOTOS of pictograms)

Beginning with junior group A "reflective circle" is held every day before breakfast with all the children present in the group. The purpose of this circle is to discuss plans for the day or any group problems. If circumstances require it, for example, some event has occurred in the group, then the “reflexive circle” can be carried out again immediately after the incident.

The circle is held in the same place, so that in the future the children will get used to discussing their problems in a circle without the presence of a teacher, in this case the circles were held in a group on the carpet. For effective discussion during the circles, we use a candle, which is placed in the center of the circle, and any object that the children pass to each other during the answers to questions, which helps the children concentrate on listening to the answers and not interrupt each other.

Reflective circles are also held after club hours. On these circles, you can find out and understand what the children liked and what they did not like.during club hours.

(PHOTO FROM SPACE AND PHOTO OF CIRCLES)

In addition to the planned ones, the topics of the "Circles of reflection" were determined by the teacher according to the circumstances, for example, if some event occurred in the group.

As a result, by the end of the school year, many children have mastered the skills of coherent speech, the ability to express their thoughts. The skills to listen to each other have been formed. Most children want to express their feelings and experiences.

September

Situation of the month "My Kindergarten»

November

Situation of the month “I am a resident globe»

2017-18 academic year of the year)

Situation of the month New Year. Magic Gifts»

2018 academic year of the year)

Situation of the month "Boys and Girls"

2018 academic year of the year)

Situation of the month "Spring is red"

The result of the "Reflexive Circles" for the year:

Children are able to communicate politely with each other and with surrounding adults. They are able to conduct a dialogue, while using various means of expression. Children listen carefully and understand each other.

Russian Academy of Sciences V.A. Trapeznikova D.A. NOVIKOV, A.G. CHKHARTISHVILI REFLECTIVE GAMES SINTEG Moscow - 2003 UDC 519 BBC 22.18 N 73 Novikov D.A., Chkhartishvili A.G. Reflexive H 73 games. M.: SINTEG, 2003. - 149 p. ISBN 5-89638-63-1 The monograph is devoted to the discussion of modern approaches to the mathematical modeling of reflection. The authors introduce a new class of game-theoretic models – reflexive games that describe the interaction of subjects (agents) that make decisions based on a hierarchy of ideas about essential parameters, ideas about representations, etc. An analysis of the behavior of phantom agents that exist in the representations of other real or phantom agents and the properties of an information structure that reflects the mutual awareness of real and phantom agents allows us to propose an information equilibrium as a solution to a reflexive game, which is a generalization of a number of well-known concepts of equilibrium in non-cooperative games. Reflective games make it possible: - to model the behavior of reflective subjects; - to study the dependence of the payoffs of agents on the ranks of their reflection; - set and solve problems of reflexive control; - uniformly describe many phenomena related to reflection: hidden control, information control through the media, reflection in psychology, works of art, etc. The book is addressed to specialists in the field of mathematical modeling and management of socio-economic systems, as well as university students and graduate students. Reviewers: Doctor of Technical Sciences, prof. V.N. Burkov, Doctor of Technical Sciences, prof. A.V. Shchepkin UDC 519 BBK 22.18 N 73 ISBN 5-89638-63-1 Chkhartishvili, 2003 2 CONTENTS INTRODUCTION .................................................. ................................................. .......... 4 CHAPTER 1. Information in decision-making .................................. ........... 21 1.1. Individual Decision Making: A Model of Rational Behavior.................................................................. ................................................. ............................... 21 1.2. Interactive decision-making: games and equilibria .............................. 24 1.3. General Approaches to Describing Awareness.................................................. 31 CHAPTER 2. Strategic Reflection....... ................................................. 34 2.1. Strategic reflection in two-person games .............................. .................. 34 2.2. Reflection in bimatrix games .............................................................. ........... 41 2.3. Limitation of the rank of reflection .............................................................. .............. 57 CHAPTER 3. Informational reflection .............................. ...................... 60 3.1. Informational reflection in two-person games .............................................. 60 3.2. Information structure of the game .............................................................. .............. 64 3.3. Information balance .............................................................. ................... 71 3.4. Graph of a reflexive game ............................................................... ........................... 76 3.5. Regular awareness structures.............................................................. 82 3.6. The rank of reflection and informational equilibrium .............................................. 91 3.7. Reflective control .................................................................. ....................... 102 CHAPTER 4. Applied models of reflexive games .................................. 102 ............. 106 4.1. Hidden control .................................................................. .................................. 106 4.2. Mass media and information management .............................................................. ...... 117 4.3. Reflection in psychology .............................................................. ........................... 121 4.3.1. Psychology of chess creativity............................................... 121 4.3 .2. Transactional analysis .............................................................. .................. 124 4.3.3. Johari window .................................................. .................................. 126 4.3.4. Ethical Choice Model .................................................................. .............. 128 4.4. Reflection in works of art............................................... 129 CONCLUSION..... ................................................. ...................................... 137 LITERATURE .......... ................................................. ................................................... 142 3 - Minnows frolic freely, this is their joy! – You are not a fish, how do you know what its joy is? “You’re not me, how do you know what I know and what I don’t know?” From a Taoist parable - The point, of course, venerable archbishop, is that you believe in what you believe in because you were brought up that way. - May be so. But the fact remains that you, too, believe that I believe what I believe, because I was brought up that way, for the reason that you were brought up that way. From the book “Social Psychology” by D. Myers on the basis of a hierarchy of ideas about essential parameters, ideas about views, etc. Reflection. One of the fundamental properties of human existence is that, along with the natural ("objective") reality, there is its reflection in consciousness. At the same time, between the natural reality and its image in the mind (we will consider this image as a part of a special - reflective reality) there is an inevitable gap, a mismatch. Purposeful study of this phenomenon is traditionally associated with the term “reflection”, which is defined in the “Philosophical Dictionary” as follows: “REFLEXION (lat. reflexio – reversal). A term meaning reflection, as well as the study of a cognitive act. The term "reflection" was introduced by J. Locke; in various philosophical systems (J. Locke, G. Leibniz, D. Hume, G. Hegel, etc.) it had different content. A systematic description of reflection from the point of view of psychology began in the 60s of the XX century (school 4 of V.A. Lefebvre). In addition, it should be noted that there is an understanding of reflection in a different meaning, related to the reflex - “the reaction of the body to the excitation of receptors”. In this paper, we use the first (philosophical) definition of reflection. To clarify the understanding of the essence of reflection, let us first consider the situation with one subject. He has ideas about the natural reality, but he can also be aware (reflect, reflect) these ideas, as well as be aware of the awareness of these ideas, etc. This is how reflective reality is formed. Reflection of the subject regarding his own ideas about reality, the principles of his activity, etc. is called auto-reflection or reflection of the first kind. Note that in most humanities studies we are talking , first of all, about auto-reflection, which in philosophy is understood as the process of thinking of an individual about what is happening in his mind. Reflection of the second kind takes place regarding ideas about reality, decision-making principles, self-reflection, etc. other entities. Let us give examples of reflection of the second kind, illustrating that in many cases the correct own conclusions can be made only if we take the position of other subjects and analyze their possible reasoning. The first example is the classic Dirty Face Game, sometimes referred to as the wise men and hats problem or the husbands and unfaithful wives problem. Let us describe it following . “Let's imagine that Bob and his niece Alice are in the compartment of a Victorian carriage. Everyone's face is messed up. However, no one blushes with shame, although any Victorian passenger would blush knowing that the other person sees him dirty. From this we conclude that none of the passengers knows that his face is dirty, although everyone sees the dirty face of his companion. At this time, the Conductor looks into the compartment and announces that there is a man with a dirty face in the compartment. After that, Alice blushed. She realized that her face was dirty. But why did she understand this? Didn't the Guide tell her what she already knew? 5 Let's follow the chain of Alice's reasoning. Alice: Suppose my face is clean. Then Bob, knowing that one of us is dirty, should conclude that he is dirty and blush. If he does not blush, then my premise about my clean face is false, my face is dirty and I should blush. The conductor added information about Bob's knowledge to the information known to Alice. Until then, she hadn't known that Bob knew that one of them was dirty. In short, the conductor's message turned the knowledge that there was a man with a dirty face in the compartment into general knowledge. The second textbook example is the Coordinated Attack Problem; there are problems close to it about the optimal information exchange protocol - Electronic Mail Game, etc. (see reviews in ). The situation is as follows. Two divisions are located on the tops of two hills, and the enemy is located in the valley. You can win only if both divisions attack the enemy at the same time. The general - the commander of the first division - sends the general - the commander of the second division - a messenger with the message: "We attack at dawn." Since the messenger can be intercepted by the enemy, the first general must wait for a message from the second general that the first message has been received. But since the second message can also be intercepted by the enemy, the second general needs to get confirmation from the first general that he received confirmation. And so on ad infinitum. The task is to determine after what number of messages (confirmations) it makes sense for the generals to attack the enemy. The conclusion is as follows: under the described conditions, a coordinated attack is impossible, and the way out is to use probabilistic models. The third classical problem is the "two broker problem" (see also speculation models in ). Suppose that two brokers playing on the stock exchange have their own expert systems that are used to support decision making. It happens that the network administrator illegally copies both expert systems and sells his opponent's expert system to each broker. After that, the administrator tries to sell each of them the following information - "Your opponent has your expert system." Then the administrator tries 6 to sell information - "Your opponent knows that you have his expert system", and so on. The question is, how should brokers use the information they get from the administrator, and what information is relevant at which iteration? Having completed the consideration of examples of reflection of the second kind, let us discuss the situations in which reflection is essential. If the only reflexive subject is an economic agent that seeks to maximize its objective function by choosing one of the ethically acceptable actions, then the natural reality enters the objective function as a parameter, and the results of reflection (representations about representations, etc.) are not elements of the objective function. Then we can say that autoreflection is “not needed”, since it does not change the action chosen by the agent. Note that the dependence of the subject's actions on reflection can take place in a situation where actions are ethically unequal, that is, along with the utilitarian aspect, there is a deontological (ethical) one - see . However, economic decisions are, as a rule, ethically neutral, so let's consider the interaction of several subjects. If there are several subjects (the decision-making situation is interactive), then the target function of each subject includes the actions of other subjects, that is, these actions are part of natural reality (although they themselves, of course, are due to reflexive reality). At the same time, reflection (and, consequently, the study of reflective reality) becomes necessary. Let us consider the main approaches to mathematical modeling of reflection effects. Game theory. Formal (mathematical) models of human behavior have been created and studied for more than a century and a half (see review in ) and are increasingly being used both in control theory, economics, psychology, sociology, etc., and in solving specific applied problems. . The most intensive development has been observed since the 40s of the XX century - the moment of the emergence of game theory, which is usually dated to 1944 (the first edition of the book by John von Neumann and Oskar Morgenstern "Game Theory and Economic Behavior"). 7 Under the game in this work we will understand the interaction of the parties whose interests do not coincide (note that another understanding of the game is possible - as "a type of unproductive activity, the motive of which lies not in its results, but in the process itself" - see also , where the concept of the game is interpreted much more broadly). Game theory is a branch of applied mathematics that studies decision-making models in the conditions of a mismatch of interests of the parties (players), when each party seeks to influence the development of the situation in its own interests. Further, the term "agent" is used to refer to the decision-maker (player). In this paper, we consider non-cooperative static games in normal form, that is, games in which agents choose their actions once, simultaneously and independently. Thus, the main task of game theory is to describe the interaction of several agents whose interests do not coincide, and the results of activity (winning, utility, etc.) of each depend in the general case on the actions of all . The result of such a description is a forecast of a reasonable outcome of the game - the so-called solution of the game (equilibrium). The description of the game is in the task the following parameters : - sets of agents; - preferences of agents (dependencies of payoffs on actions): it is assumed (and this reflects the purposefulness of behavior) that each agent is interested in maximizing his payoff; - sets of admissible actions of agents; - awareness of agents (the information that they have at the time of making decisions about the chosen actions); - the order of functioning (the order of moves - the sequence of choice of actions). Relatively speaking, the set of agents determines who participates in the game. Preferences reflect what agents want, sets of allowed actions what they can do, awareness reflects what they know, and order of operation reflects when they choose actions. 8 The listed parameters define the game, but they are not sufficient to predict its outcome - the solution of the game (or the equilibrium of the game), that is, the set of actions of agents that are rational and stable from one point of view or another. To date, there is no universal concept of equilibrium in game theory – taking certain assumptions about the principles of decision-making by agents, one can obtain various solutions. Therefore, the main task of any game-theoretic research (including the present work) is the construction of an equilibrium. Since reflexive games are defined as such an interactive interaction of agents in which they make decisions based on the hierarchy of their representations, the awareness of agents is essential. Therefore, let us dwell on its qualitative discussion in more detail. The role of awareness. General knowledge. In game theory, philosophy, psychology, distributed systems, and other fields of science (see review in ), not only agents' beliefs about essential parameters are important, but also their beliefs about other agents' beliefs, and so on. The set of these representations is called a hierarchy of beliefs and is modeled in this paper by the information structure tree of a reflexive game (see Section 3.2). In other words, in situations of interactive decision-making (modeled in game theory), each agent must predict the behavior of opponents before choosing his action. To do this, he must have certain ideas about the vision of the game by opponents. But the opponents must do the same, so the uncertainty about which game will be played creates an endless hierarchy of representations of the participants in the game. Let's give an example of a view hierarchy. Suppose that there are two agents, A and B. Each of them can have their own non-reflexive ideas about the indefinite parameter q, which we will call the state of nature (state of nature, state of the world). We denote these representations by qA and qB, respectively. But each of the agents within the framework of the process of reflection of the first rank can think about the ideas of the opponent. These representations (representations of the second order) are denoted by qAB and qBA, where qAB are agent A's representations of agent B's representations, 9 qBA are agent B's representations of agent A's representations. second rank) can think about what the opponent's ideas about his ideas are. This is how representations of the third order, qABA and qBAB, are generated. The process of generating representations of higher orders can continue indefinitely (there are no logical restrictions on increasing the reflexion rank). The totality of all representations - qA, qB, qAB, qBA, qABA, qBAB, etc. - forms a hierarchy of views. A special case of awareness is when all representations, representations about representations, etc. coincide to infinity – is common knowledge. More correctly, the term "common knowledge" is introduced in to denote a fact that satisfies the following requirements: 1) it is known to all agents; 2) all agents know 1; 3) all agents know 2, and so on. ad infinitum The formal model of general knowledge was proposed in and developed in many works - see . Models of agents’ awareness – the hierarchy of representations and general knowledge – in game theory are, in fact, entirely devoted to this work, so we will give examples illustrating the role of general knowledge in other areas of science – philosophy, psychology, etc. (see also review ). From a philosophical point of view, common knowledge was analyzed in the study of conventions. Consider the following example. It is written in the Rules of the Road that each road user must comply with these rules, and also has the right to expect that other road users observe them. But other road users also need to be sure that others follow the rules, and so on. to infinity. Therefore, the agreement to "observe traffic rules" should be common knowledge. In psychology, there is the concept of discourse - “(from Latin discursus - reasoning, argument) - verbal thinking of a person mediated by past experience; acts as a process of associated logical 10

Along with reflexive games, a possible method of game-theoretic modeling under conditions of incomplete awareness is bayes games, proposed in the late 1960s. J. Harshanyi. In Bayesian games, all private (i.e., not general knowledge) information that an agent has at the time he chooses his action is called type agent. Moreover, each agent, knowing its type, also has assumptions about the types of other agents (in the form of a probability distribution). Formally, a Bayesian game is described by the following set:

• - many N agents;
• - sets /?, possible types of agents, where the type of the /th agent

many X' = J-[ X x admissible action vectors of the agent

• -a set of objective functions /: R'x X'-> 9? 1 (the objective function of an agent generally depends on the types and actions of all agents);
• - representations F, (-|r,) e D(/?_,), /" e N, agents (here, /?_ denotes the set of possible sets of types of all agents, except for the /-th, R.j= P R t , and D(/?_,) denotes the set

in all possible probability distributions on /?_,). The solution to the Bayesian game is Bayes-Nash Equilibrium, defined as a set of strategies of agents of the form X*: R, -> X h i e N,

which maximize the mathematical expectations of the corresponding objective functions:

where jc denotes the set of strategies of all agents, except for the j-th one. We emphasize that in the Bayesian game, the agent's strategy is not an action, but a function of the dependence of the agent's action on its type.

J. Harshanyi's model can be interpreted in different ways (see). According to one interpretation, all agents know the a priori distribution of types F(r) e D (R') and, having learned their own type, they calculate the conditional distribution from it using the Bayes formula Fj(r.i| G,). In this case representations of agents (F,(-|-)), sW are called agreed(and, in particular, are common knowledge - each agent can calculate them, knows what the others can do, etc.).

Another interpretation is as follows. Let there be some set of potential participants in the game of various types. Each such “potential” agent chooses his strategy depending on his type, after which he randomly chooses P"actual" participants in the game. In this case, the representations of agents, generally speaking, are not necessarily consistent (although they are common knowledge). Note that this interpretation is called playing Selten(R. Zelgen - Nobel Prize in Economics 1994, together with J. Nash and J. Harshanyi).

Now consider a situation where conditional distributions are not necessarily common knowledge. It is convenient to describe it as follows. Let agents' payoffs depend on their actions and on some parameter in e 0 (“states of nature”, which can also be interpreted as a set of types of agents), the value of which is not common knowledge, i.e., the objective function of the /th agent has the form f i (0,x x ,...,x n): 0 x X'- ""L 1, /" e N. As was noted in the second chapter of this work, the agent's choice of his strategy is logically preceded by informational reflection - the agent's thoughts about what each agent knows (assumes) about the parameter 0, as well as about the assumptions of other agents, etc. Thus, we come to the concept the agent's awareness structure, which reflects his awareness of the unknown parameter, the representations of other agents, etc.

Within the framework of probabilistic awareness (representations of agents include the following components: a probabilistic distribution on a set of states of nature; a probabilistic distribution on a set of states of nature and distributions on a set of states of nature that characterize the representations of other agents, etc.), a universal space of possible mutual representations (universal beliefs space). At the same time, the game is formally reduced to a kind of "universal" Bayesian game, in which the agent's type is his entire structure of awareness. However, the proposed construction is so cumbersome that it is apparently impossible to find a solution to the "universal" Bayesian game in the general case.

In this section, we will confine ourselves to considering two-person games, where agents' representations are given by a point structure of awareness (agents have well-defined ideas about the value of an indefinite parameter; about what the opponent's (also well-defined) representations are, etc.) Taking into account These simplifications, finding the Bayes-Nash equilibrium is reduced to solving a system of two relations that define two functions, each of which depends on a countable number of variables (see below).

So, let two agents with objective functions participate in the game

and the functions f and many X b 0 are common knowledge. The first agent has the following representations: the undefined parameter is equal to 0 e 0; the second agent believes that the undefined parameter is equal to in 2 e 0; the second agent thinks that the first agent thinks that the undefined parameter is in 2 e 0, etc. Thus, the point structure of awareness of the first agent /, is given by an infinite sequence of elements of the set 0; let, similarly, the second agent also has a point structure of awareness 1 2:

Let us now look at the reflexive game (2)-(3) from the "Bayesian" point of view. The agent's type in this case is its awareness structure /, /=1, 2. To find the Bayes-Nash equilibrium, it is necessary to find the equilibrium actions of agents of all possible types, and not just some fixed types (3).

It is easy to see what the distributions F,(-|-) will be in this case from the definition of equilibrium (1). If, for example, the type of the first agent 1={6, 0 !2 , 0w, ...), then the distribution Fi(-|/i) assigns the probability 1 type of opponent / 2 =(0 | 2 , 012b 0W2, ) and the probability 0 for other types. Accordingly, if the type of the second agent ^2 = (02> $2b Fig*)> then the distribution F 2 (-|/ 2) assigns probability 1 to the opponent 1=(in 2 , 0 212 , 02:2i ) and probability 0 for other types.

To simplify the notation, we will use the following notation:

Let us also introduce the notation

In these notations point the Bayes-Nash equilibrium (1) is written as a pair of functions ((pi-), i//(-)) satisfying the conditions

Note that within the point structure of awareness, the 1st agent is sure that the value of the indefinite parameter is 0 (regardless of the opponent's ideas).

Thus, to find equilibrium, it is necessary to solve the system of functional equations (4) to determine the functions (R(-) and!//( ), each of which depends on a countable number of variables.

Possible structures of awareness may have a finite or infinite depth. Let us show that the application of the Bayes-Nash equilibrium concept to agents with an infinite depth awareness structure gives a paradoxical result - any admissible action is equilibrium for them.

Let us define the concept of finiteness of the depth of the awareness structure in relation to the case of a game with two participants, when the awareness structure of each of them is an infinite sequence of elements from 0.

Let the sequence T= (t j) " =[ elements from 0 and a non-negative integer to. Subsequence (o k (T) = (t t) /=i+1

we will call k-ending sequences T.

We will say that the sequence T It has endless depth if for any P there will be k>n such that the sequence with to (T) does not match (meaning the usual element-wise match) with any of the sequences in the set a>u(T)=T, (0 (T),..., (o n (T). Otherwise, the sequence T It has final depth.

In other words, a sequence of finite depth has a finite number of pairwise distinct endings, while a sequence of infinite depth has an infinite number of them. For example, the sequence (1, 2, 3, 4, 5, ...) has infinite depth, while the sequence (1, 2, 3, 2, 3, 2, 3, ...) has finite depth.

Consider the game (2) in which the objective functions f, f2 and many X, X 2, 0 have the following property:

(5) for any A" | e X, x 2 e X 2, in e 0 sets

Conditions (5) mean that for any in e© and any action Xi e X the second agent has at least one best answer and, in turn, the action itself X is the best response to some action of the second agent; likewise, any action

X 2 G X 2 .

It turns out that under conditions (5) in game (2) any the action of an agent with an infinite depth awareness structure is equilibrium (i.e., it is a component of some equilibrium (4)). The ego is true for both agents; for definiteness, we formulate and prove the assertion for the first one.

Statement 2.10.1. Let the game (2) in which conditions (5) be satisfied, have at least one point Bayes-Nash equilibrium (4). Then for any information structure of infinite depth 1 and any % e X there is an equilibrium (*,*( ) > x*(-)), in which x*(/,) =x-

The idea of ​​the proof is to construct the corresponding equilibrium constructively. Let us fix an arbitrary equilibrium (1. By virtue of conditions (4), the value of the function φ ( ) took on the structure 1 meaning X-

We preface the proof of Assertion 2.10.1 with four lemmas, for the formulation of which we introduce the notation: if p=(p,...,/>„) is finite, and T=(/.)", - an infinite sequence of elements

from 0, then pT= 0, h, ...)

Lemma 2.10.1. If the sequence T has infinite depth, but for any finite sequence R and any to subsequence rso k (T) also has infinite depth.

Proof. Because the T has infinite depth, it has an infinite number of pairwise different endings. When moving from T to s k (t) their number is reduced by no more than to, still remaining infinite. When moving from with to (T) to ry to (T) the number of pairwise distinct endings obviously does not decrease.

Lemma 2.10.2. Let the sequence T represent in the form T=rrr where R - some non-empty finite sequence. Then T has finite depth.

Proof. Let R has the form p=(p, Then the elements of the sequence T related by the relations t i+nk = t, for all integers / > 1 and to > 0. Take an arbitrary y-ending, y > P. Number j uniquely representable in the form j = i + p k, where /e(1, ..., "), A" > 0. It is easy to show that a>(T) = (o,(T) for any whole m> 0 running = t i+ „ k+m =

Given the arbitrariness j we have shown that the sequence T no more P pairwise distinct endings, i.e., its depth is finite.

Lemma 2.10.3. Let for the sequence T the identity T = p T, where R is some non-empty finite sequence. Then T has finite depth.

Proof. Let p =(/? b ...,R"). We have:

T=r T=rr T=rrr T=rrrr T=... . Thus, for any integer k> 0 fragment (/„*+, ..., /„*+„) matches (p b That's why

T represent in the form T = prr... and, according to Lemma 2.10.2, has finite depth.

Lemma 2.10.4. Let the sequence T the identity p T = q T, where R and q are some non-identical non-empty finite sequences. Then T has finite depth.

Proof. Let R= (/;, . and q = (qb ..., qk). If a n = k, th, obviously, identity pT=q T cannot be executed. Therefore, consider the case pFc. Let for definiteness n > k. Then p = (q u ..., q k ,p k+ , ...,R"), and from the condition pT=q T follows that d T \u003d T, where d = (j) k+ 1 , ...,p p). Applying Lemma 2.10.3, we get that the depth of the sequence T finite.

Proof of Statement 2.Yu.L. Let there be an arbitrary structure of information awareness of the first agent of infinite depth - for uniformity with Lemmas 2.10-2L0.4, we will denote it not /, but T \u003d (t, t 2,. By the condition of the assertion, there is at least one pair of functions!//( )) satisfying relations (4); fix any of these pairs. We set the value of the function f( ) on the sequence T equal

X". φ(T) = x(hereinafter, for "newly defined" functions we will use the notation f( ) and f( )) Substituting T as function argument f( ) in relations (4), we obtain that the value f(t) = x is related (due to (4)) with the values ​​of the function f( ) on the sequence (0 (T), and also on all such sequences 7”,

FOR WHICH CO(T')= T.

We choose the values ​​of the function f( ) on these sequences in such a way that conditions (4) are satisfied:

where t e Q; from (5) it follows that the ego can be made. If the set BR"(t,x) or BR2(t,x) contains more than one element, take any of them.

p(* 3 ,/ 4 ,...) € BR 2 "(t 2, a, substituting (t, t2, t2,...), choose

Continuing to substitute the already obtained values ​​into relations (4), we can successively determine the values ​​of the function f( ) on all sequences of the form

where (t + k)- odd, and function values f(?) on sequences of the form (6) with even (t + k). Further, we will assume that in (6) at t> 1 in progress Ф t m ., - then the representation in the form (6) is

unambiguous.

The algorithm for determining the value of functions on sequences of the form (6) consists of two stages. At the first stage, we assume f(T)=x and determine the values ​​of the corresponding functions on the sequences w,n(r) = ( t„„ t m+ 1, ...), m> 1 (i.e. at k= 0) by alternately applying the mappings DD, 1 and 5/?, 1 .

At the second stage, to determine the value of the corresponding functions on sequences (6) with to > 1 we proceed from the value determined at the first stage on the sequence (t„„ t„,+ 1, ...), applying alternately the mappings BR and BR2.

According to Lemma 1, all sequences of the form (6) have infinite depth. According to Lemma 4, they are all pairwise distinct (if any two sequences of the form (6) coincided, this would contradict the infinity of depth). Therefore, determining the values ​​of the functions f( ) and f( ), we do not risk assigning to the same argument different meanings functions.

Thus, we have determined the values ​​of the functions f( ) and f( ) on sequences of the form (6) in such a way that these functions still satisfy conditions (4) (i.e., they are a point Bayes-Nash equilibrium) and, moreover, f(T) =%. Assertion 2. K). 1 is proven.

So, the notion of point Bayes-Nash equilibrium was introduced above. It has been proven that when additional conditions(5) any admissible action of an agent with an infinite depth of awareness structure is an equilibrium one. (All considerations were carried out for a game with two participants, however, it can be hypothesized that the result obtained can be generalized to the case of a game with an arbitrary number of participants.) This circumstance, apparently, indicates the inexpediency of considering structures of infinite depth as in terms of information equilibrium , and in terms of the Bayes-Nash equilibrium.

More generally, it can be noted that the proved statement is an argument (and not the only one, see, for example, sections 2.6 and 3.2) in favor of the inevitable limitation of the rank of information reflection of decision-making subjects.

reflexively- business games

The effective solution of intraschool problems is largely determined by the degree of involvement of all participants in this process. educational process, their interest in the success of the business, the opportunity to acquire personal success in solving common tasks. In this regard, business games can be considered one of the optimal forms of collective organization for solving current and future problems of the school.

Consider the most common games used in practice.

Organizational and activity games. The creator of this type of productive games was. The main goal and purpose of organizational and activity games is the development of the mental activity of the participants in the game themselves. This game is characterized by a tense rhythm of work, the number of participants reaches 600, the result of the game is, first of all, some new knowledge, understanding. The main methods include "brainstorming", discussion, "round table", analysis of specific situations, synectics (figurative expression of the problem), positional conflict. Reflection acts as a means of awareness and reflection by the players of their own thinking.

Innovative Games developed. This form of the business game emerged from the organizational and activity one, however, in the game the emphasis is not on the study of problems, but on their solution (the question “why?” is mixed with the question “how?”. The number of participants is 25 people, educational and consulting rooms are used, and also transformed classic game methods (discussion, brainstorming).

Practical business games were first played and explained. The positional nature of a practical business game is based not on differences in subjective thinking, but on the confrontation of the interests of competitors. In this game, various forms of group work are activated.

Problem business games– were conducted for the first time by specialists from the Saratov University. During the game stage, the following methods of collective mental activity are used: brainstorming, simulation games, socio-psychological training, synectics, multi-level reflection, press conference, etc.

Problem-activity games began to be developed and tested in the 90s at the Moscow and Chelyabinsk Pedagogical Universities. The purpose of the problem-activity game as a method of intra-school management is to find an effective solution to the actual problems of the educational process by involving school teachers in the game space.

One of the varieties of problem-activity games are p reflective business games.

The reflexive business game (RDG) is a modern active form of work with participants in the educational process, which is the organization of a special reflective environment in which each participant not only acquires a new cognitive, behavioral experience, but also becomes the initiator of his own personal development and development of its partners.

In contrast to the above productive business games, RDI is focused primarily on participants in the educational process. At the same time, the solution of business educational problems is provided through the use and development of the possibilities of the reflective consciousness of the participants. Socially developing and personally developing tasks in this type of games are of the same importance as obtaining a business creative product. The integration of business and developmental tasks is provided by a special technology of implementation, in which much attention is paid to the implementation of reflexive forms of interaction.

The basic concept that determines the meaning of such an organization of the learning space is reflection. According to the words, reflection is a process of self-knowledge by a person of internal mental states, as well as a person's awareness of how he is actually perceived and evaluated by other people or a community of people. According to PM. Andreeva, reflection is not just knowledge and understanding of the other, but knowledge of how the other understands me, a kind of double process of mirror reflections by people of each other. In order to give a more complete picture of the essence of reflection, we give another definition of reflection given by: “Reflection is a human ability that allows a person to make his thoughts, emotional states, actions, relationships, himself the subject of special consideration (analysis and evaluation) and practical transformation.

The above definitions of reflection allow us to highlight some features of the reflexive environment, and hence the reflexive business game, which distinguish it from traditional learning environments.

So, the reflexive nature of the business game is provided by:

Initiation problem situations expanding participants' understanding of themselves and others;

Considering any problem not as a difficulty, “a barrier, but as an opportunity for further development;

Creation of conditions for cooperation, interaction, exchange of opinions and other forms of social activity;

Modeling situations that correspond to the maximum extent to the tasks and interests of the participants;

The use of positional interaction, in which the problem under consideration is studied from various role, conceptual positions;

Creation of conditions for deep understanding, analysis and rethinking by the participants of their empirical experience;

Encouraging innovative approaches to problem solving;

The development of the participants' skills of mutual understanding, active listening, openness to experience;

The initiation of a holistic perception of people and situations, which allows us to consider the polar possibilities and options for their mutual transitions as sources of development.

The business orientation of the game is determined by its focus on performance in relation to the set practice-oriented tasks. The business tasks of the game can be aimed at acquiring professional knowledge, skills and abilities by the participants; for the development of a certain creative product (in the form of a project, model, recommendations, educational and methodological complex, etc.); to assess professional competence, the level of knowledge, skills, etc.; to solve specific problems of the team (development of rules of conduct in the team, selection of a representative from the group, formation of an administrative team, designing a model of the psychological service of an educational institution, determining specific ways to resolve a group conflict, developing a school charter, etc.).

The integration of the business orientation of the game and the reflexive nature of the environment in which the solution of practice-oriented tasks takes place ensures to the maximum extent not only the effectiveness of their solution, but also the personality-oriented

the nature of the organization of this process, as well as the satisfaction of the participants with the opportunity to make their special contribution to the solution of the tasks set.

When preparing a reflexive-business game, the leader should pay special attention to the following points that ensure the success of its implementation:

Compliance of the goals of the game with the interests and needs of the participants. This is ensured by a clear orientation of the game to a possible social order (on the part of teachers, schoolchildren, the administration of the educational institution, etc.).

Detailed development of the game scenario, which should provide not only a clear correspondence between the goals of each stage of the overall goal of the game, the forms of work, but also the regulation of the stages and exercises, the availability of handouts.

If RDI provides for the development of any creative product, then the leader must first develop criteria for its evaluation, approximate components that will allow directing the course of the game in a constructive direction.

For a clearer organization of the RDI and maintaining the creative activity of the participants, it is important to provide them with such handouts that would allow them not to scatter their attention on routine work (drawing tables, graphs, drawing up long sentences, etc.), but productively fix ideas on competently. prepared handout.

For a broader initiation of innovative approaches to solving the tasks set, it is important for the facilitator to prepare problematic questions in advance that would destroy the stereotypes of participants' perception of problems and situations, encourage their ability to find meaning in nonsense, certainty in uncertainty, harmony in chaos, and stability in fluidity. and vice versa.

In order for participants to better assess the effectiveness and scope of their work, you can use large sheets whatman paper, bright felt-tip pens to visually effectively demonstrate the work in front of the entire audience.

A surge in the creative activity of RDI participants is often associated with the use of reference to cultural and historical images in the game (search and selection of a cultural analogue - a historical hero or plot that fully reflects the phenomenon under study), a visual representation of the problem under study - in the form of a socio-dramatic improvisation, drawing: revealing implicit meanings and contexts of the presented images.

The most important form in RDI is positional interaction. It is organized different ways: by setting the leading positions within each microgroup, choosing by the members of the microgroup those role positions that are most interesting to them, by setting the position of the microgroup (in this case, members of the same microgroup discuss from the same positions), etc.

The main functions of the leading RDI include:

Organization of purposeful collective activity of participants;

Strict observance of the stages of the game and control over the regulations for the implementation of tasks;

Encouraging innovative approaches to problem solving;

Help participants express their point of view;

Fixing (if necessary) the results of the discussion;

Explanation and clarification of the participants' statements;

Assistance in collecting the data needed to solve problems;

Summarizing the discussion of the issue;

Prevention of attempts to divert the course of the game into non-constructive

A clear and understandable statement of the final and intermediate

conclusions and results;

Instilling in the participants confidence in the importance of their opinions and decisions.

When implementing these functions, the RDI leader should not impose his opinion, assumption, conclusions on the participants. It is important for the facilitator, on the one hand, to consistently implement the strategy of the game, to keep it heated, not to be led by the audience in matters of general goal-setting, and on the other hand, to skillfully use the results of group work, hear and understand the participants, be flexible and ready for tactical changes. in Game.

Efficiency, colorfulness, practical value of the reflexive-business game are given by those exercises, techniques, methods of work that, in fact, fill it with content. We list the most common of them: discussion of the problem in microgroups, creation of graphic images, positional solution technique, personal-perspective reflection, individual and group analysis of team work, ranking the results of group work, analytical micro essays, group drawing, reflexive diagnostics, social design, reflexive methods. inversions, graphic modeling, reflexive analysis of obstacles, behavior training, identification of expectations, role play, dramatization, focus interviews, etc.

Reflexive business games can be considered a fairly new, but extremely relevant form of work with participants in the educational process. Their use allows not only to increase the professional competence of teachers, but also to introduce active, democratic forms of interaction into pedagogical practice, the conductors of which can be those teachers and administrators of educational institutions who have felt the effectiveness of collective forms of problem solving in the course of reflexive business games.

In our opinion, the reflexive-business game (RDG) is one of the modern educational forms of work with schoolchildren, which allows not only to create a situation for the child's personal development through the expansion of his image of "I", but also to contribute to the formation of a children's community, characterized by mutual trust, responsibility, ability for constructive cooperation of its members.

The reflexive-business game actualizes a wide range of sources for the development of its participants: reflexive consciousness, positive "I"-concept, personal attitudes towards acceptance, understanding and openness of partners. This game provides students with the opportunity not only to think, but also to act both in their own interests and in the interests of the group.

The reflexive nature of games is ensured by the organization of such a communicative space in which there is an active discussion in microgroups of problematic issues related to the business and personal goals of the game; conditions are created for better self-recognition by schoolchildren, for mutual knowledge, for the child to discover himself for another and others for himself.

The proposed projects of reflexive business games can be recommended for implementation in classroom groups, school assets, school government committees, etc.

Development of GROUP rules of conduct

The presented RDI can be held at the beginning of the school year in the classroom, on the school’s asset, in the KVN team, etc. It allows schoolchildren to feel responsible for their actions, belonging to the norms school life. Such a game can become a step towards the democratization of intra-school relations and, at some stage, turn into a school-wide game to develop intra-school norms of behavior.

It should be noted that the algorithm of the game "Development of group rules of behavior" can be used to develop rules for handling a book, rules for relations between people, rules for a healthy lifestyle, etc.

Game Goals:

Development of rules of conduct in the class (group);

The development of the reflective consciousness of students and the expansion of their

image of "I"

Development of cooperation skills.

Number of participants: from 6 to 24 people (one class, group).

Age of participants: 2-11th grade.

Stages of the game

1. Warm up

Removal of emotional tension;

Development of positive interest in the partner;

Expansion of schoolchildren's ideas about themselves, about comrades, about class life.

Group development of a set of rules of conduct, the observance of which should contribute to the cohesion of the class (group);

Means: group problem work; ranking the results of group work.

Expected result: a set of rules of conduct in the class (group); positive attitude of everyone to the list of rules received.

Z. Reflexive

Expansion of the image of the "I" of the participants;

Development of reflective consciousness;

Development of readiness to act in accordance with the rules and readiness to improve these rules;

Development of the "We" image.

Means: self-assessment and mutual assessment, personal-perspective reflection.

Expected result: willingness to act in accordance with the rules; readiness to learn from comrades and teach comrades to observe the rules through their own behavior; expanding understanding of self and others; readiness for further cooperation.

Game progress

1. Warm up. "Communication Pinwheel"

Participants form two circles: inner and outer, sitting facing each other in pairs. At the signal of the leader, the participants sitting in the outer circle perform the task of the leader regarding the partner opposite (in pairs), then the participant from the inner circle does the same and, finally, exchange of impressions. It is important that the partner being described does not interfere with the speaker's speech, and, perhaps, even writes down personally important information for him. After completing each task, the participants in the outer circle move one place (for example, clockwise). Thus, new pairs are formed.

1) describe the appearance of the partner;

2) make a guess about his hobby;

H) name the strong side of the partner's character;

4) name weak side his character;

5) to assume that the partner appreciates people the most;

6) suggest what irritates him most of all in people;

7) name the role that the partner most often plays in the group;

8) describe his contribution to the affairs of the class or school;

9) give advice to a partner;

10) suggest what you can learn from your partner.

2. Development of group rules of conduct

The facilitator invites each microgroup (during the discussion) to write 6-7 rules of behavior in the group (class), which, in their opinion, would contribute to the comfort of students in the classroom and their cohesion. At the same time, the facilitator draws the attention of schoolchildren to the fact that the rules are formulated through actions, and not through the implementation of some personal qualities of students. For example, the rule “Be attentive to a friend” cannot be considered Constructive, because each person puts his own meaning into the word “attentive”. As a result, this rule becomes vague and can be implemented through many actions. In this regard, it is initially difficult to implement. An alternative to it could be a more constructive rule: "Offer help if you see that a friend needs it."

10-12 minutes are allotted for work in microgroups.

The facilitator invites a representative from each microgroup to name the rules of conduct developed as a result of the discussion. The facilitator writes them down on the board. Duplicate rules are not recorded. As a result, 13-20 rules are fixed on the board on average.

The facilitator invites each participant in the game to choose from the list of rules received three, in their opinion, the most important. Each participant can write down these rules (or their serial number) on a separate sheet.

Then the facilitator ranks the list of rules developed by the group using the following technique: first, he asks those students who chose the first rule to raise their hands - and puts the corresponding number of votes on the board next to its wording, then those who chose the second rule raise their hands - and on the corresponding number of votes is marked on the board, and so on. As a result, next to the wording of each rule, there should be a number on the board that characterizes the number of choices for this rule.

The host, with the support of the group, selects from the list of 6-7 rules that received the most votes, and simply erases the rest of the rules from the board. As a result, 6-7 winning rules remain on the board.

Next, the facilitator invites each student to write down the winning rules in a notebook, and then concludes that these rules of behavior were developed by the students themselves and thus they took on. responsibility for their observance. Now the class, by common agreement, must learn to live by these rules, Supporting each other.

At the end of the main stage, you can invite students to perform some kind of ritual action: swear aloud in chorus to follow these rules, visualize them (you can with illustrations) and hang them in the classroom.

H. Reflective stage

The facilitator invites each participant in the game to work with personal sheets of rules as follows:

Put an exclamation point next to those rules, the implementation of which will not be difficult for the student;

Put a question mark next to those rules, the observance of which should require certain efforts and, possibly, internal work on oneself;

Write next to the question marks the names or surnames of those people (comrades, teachers, parents, etc.) who can teach you to follow these rules. It is better if the teacher asks the students first of all to pay attention to their classmates as teachers in observing the rules.

After the work proposed by the leader with the sheets of rules has ended, each participant in the game voices their answers. In general, the performance of each student may look like this: “The easiest thing for me to do is to follow ... the rules. Difficulties can cause ... rules. But I will learn the first rule from you, Sveta, because... . And it will be easier for me to learn the third rule from Cyril, since. ."

The leader, finishing the game, reminds the students that the developed list of rules cannot be considered final. In a month it is necessary to meet again and discuss the effectiveness of these rules and the degree of their influence on the comfort of staying in a group (class).

Choice of a leader (representative) from a class

The reflexive-business game "Selecting a leader (representative) from a class" is similar in algorithm to the previously presented game, only the reflexive stage is changed. This game can be used as a means of democratically choosing a representative from a class to the School Council, to a representative event, choosing intra-class positions, etc. Similar game can be used repeatedly depending on the goals of the representation. This will allow to identify many positive leaders in the class who will be able to realize their abilities in their area of ​​competence. Such a game helps schoolchildren to better know and understand themselves, enriching this knowledge with the opinion and attitude of their comrades; think about your abilities, about your role in the life of the class and school.

Game Goals:

The choice of a leader corresponding to the goals of the representation;

Expanding the participants' self-image;

Opening and presentation by the participants of their own leadership

Development of a positive attitude towards a partner;

Development of the ability to cooperate;

Development of readiness to be controlled by a positive leader;

Development of group cohesion.

Number of participants: from b to 24 people (one class, group).

Age of participants: 2-11th grade.

Stages of the game

1. Warm up

Development of positive interest in the partner;

Expansion of schoolchildren's ideas about themselves, about comrades, about the life of the class and school.

Means: psycho-training exercises.

Expected result: creation of a friendly atmosphere in the group and increased interest in further work.

Development of a complex of personal qualities corresponding to the leader-representative;

Development of group discussion and active listening skills.

Funds:

Group problem work;

Ranking the results of group work.

Expected Result:

Development of a complex of personal qualities of a leader - a representative of the class;

The positive attitude of each to the resulting list of qualities.

Z. Reflexive

Expansion of the image “I am the participants;

Correlating your idea of ​​yourself with the ideal image of a leader-representative;

Development of the "We" image.

Funds:

Self-assessment and mutual assessment;

Personal perspective reflection.

Expected results:

Unanimous agreement of the group in choosing a positive leader according to previously developed personal qualities;

Willingness to trust the leader's decisions and delegate responsibility within the framework of the goal;

Expanding understanding of self and others;

Readiness for further cooperation.

PROGRESS OF THE GAME

1. Warm up

As a warm-up exercise, we can offer schoolchildren to depict the human body in the form of a group “sculpture”. Each participant, as a result of a group discussion or on his own initiative, chooses some organ, part of the body, the function of which he performs in the group (or maybe he wants to perform, for example, the heart, spine, hands, eyes, skin ...). The sculpture may not include a guide, who will then explain the reason for each participant's stay in this sculpture. Sculpture can be both static and dynamic. The leader does not interfere in the process of distribution of roles within the group, but observes the behavior of each participant. If the group is large (for example, a class), then it is advisable to divide it into two subgroups. It should be noted that the facilitator can give the task to portray the group, the class as it is now (the participants perform exactly the functions in the group, for example, “My class is now”), and the ideal group, class, what you can strive for - “Class, which we would like to see ideally (the participants could perform these functions in order to make the group work more efficiently).

After the sculpture is made, the guide explains why this particular participant became this particular “organ”. Then the facilitator turns to each participant in the sculpture and asks him how comfortable he feels in this role and which “organ” he would choose himself.

As an exercise, you can offer a model of the solar system with planets and satellites, a model of a car, etc.

2. The choice of a representative from the class

The group is divided into microgroups of 4-5 people each. Sheets and pens are handed out to small groups.

The facilitator invites each microgroup (after discussion) to write down 3 character traits and 3 skills that a person who is most worthy of being a representative of the class should possess. It is advisable to pre-divide the sheets distributed in microgroups into two parts: “Character Traits” and “Skills”. To work

in microgroups 10-12 minutes are allotted.

The facilitator invites a representative from each microgroup to name the character traits and skills of the future leader developed as a result of the discussion. The facilitator writes them down on the board, dividing them into two columns. As a result, on the board, on average, 10 character traits and 10 skills are recorded, which, according to the group, are inherent in the future leader.

The facilitator invites each participant in the game to choose from a list of 3 character traits and 3 skills that, in their opinion, best correspond to their idea of ​​\u200b\u200bthe ideal representative.

Then the facilitator ranks the list developed by the group using the following technique: he asks those students who chose the first character trait on the list to raise their hands, and puts the corresponding number of votes next to it; then those who chose the second trait raise their hands, and so on. As a result, next to each character trait and with each skill, there will be a number characterizing the number of choices on the board.

The host, with the support of the group, selects from the list of 3 character traits and 3 skills that received the most votes, the rest are simply erased from the board. Thus, on the board are the names of three character traits and three skills that, in the opinion of the group, their future leader should possess.

Further, the facilitator, using the finally selected characteristics of the future representative, synthesizes them into an emotionally colored psychological portrait, while paying attention to the fact that such a psychological portrait is ideal for this particular group and for the given goals.

3. Reflective stage

The group is divided into microgroups. The facilitator invites all participants in the game to draw the following table in their notebooks (the table can be prepared in advance and distributed to the participants).

Self-assessment and mutual assessment of participants

In the leftmost column of the table, the participants in the game rewrite the list of 3 character traits and 3 skills of a representative leader compiled by the group on the board. Then each student evaluates the severity of these qualities in himself on a 7-point scale and writes the results in the 2nd column (Self-assessment) of the table.

Each participant is evaluated on a 7-point scale by the members of his microgroup for the degree of manifestation of the qualities of a leader-representative. The evaluation results are recorded in the 3rd column of the table (Evaluation of others).

The second procedure can be carried out in different ways. Experience has shown that the most effective are the following:

The student being assessed goes some distance from the microgroup, the other participants evaluate him, write down the result in his table, and then invite a friend and show him the resulting points:

Each member of the microgroup evaluates a comrade, then the arithmetic mean of all estimates is found, which is recorded in the third column of the evaluated. The proposed methods allow more objectively, with minimal intervention of the person being assessed, to carry out the assessment procedure. Thus, the second and third columns of the table are filled. Each participant then totals the total scores for each

quality and skill and divides by 2 to get the final value (4th column). In essence, the final value for each quality is the arithmetic mean of the student's self-assessment, expressed in points, and the assessment of this quality by his comrades. Thus, the fourth total column is filled. After the final marks for each quality are received, the students summarize them vertically. The generalized result is recorded in the "Total" line. It is clear that the maximum final value, demonstrating the severity of the selected k” qualities, should be b x 7 = 42 points.

The facilitator invites the five participants who have scored the highest total points to come to the board.

The facilitator notes that the graduating students objectively correspond to the maximum extent to the role of a leader-representative (by points). However, in order to choose the best of them, they need to make a positive impression on others, to really show the qualities highlighted by the group. To do this, each applicant must give a speech within one minute in which he convinces others of why he should be chosen.

After the speeches of all candidates are heard, the group votes for one of them. The voting procedure can be carried out in this way: each candidate is assigned a number, and paper squares are distributed to the participants. The participant must write on one of the sides of this box the number corresponding to the number of the candidate chosen by him. Then the squares are folded into a box. The facilitator lays out the squares in piles corresponding to the numbers of candidates (you can elect a counting commission). The candidate with the most votes is considered elected. Thus, the group chooses its leader-representative.

Let's agree

This game, in our opinion, is quite relevant for schoolchildren. different ages, which is due to the following factors.

Participation in the game actualizes a sense of adulthood in schoolchildren, which is realized through his truly adult behavior (responsible, partner, respectful, constructive) in the process of negotiating.

Negotiating in the game, carried out in conditions of time pressure and in the absence of competition, reduces the effect of the protective mechanisms of the participants and stimulates their creative possibilities.

Staying students in three different positions in the same situation allows participants to learn to understand and respect the interests of partners.

The role of the observer used in positional interaction and play makes the initial analytical act directed at the action of another, which serves as the basis for the students to analyze their experience of behavior in an interaction situation.

The reflexive stage of the game actualizes in students the desire to negotiate more in problem situations, to consider their classmates not only as potential business partners, but also as teachers in the art of negotiation.

The described game can be modified in relation to the composition of microgroups. Parents and teachers can be included in microgroups, they can be created not arbitrarily, but in accordance with pedagogical goals (for example, outsiders can be combined in one microgroup with those students they have chosen in the sociometric research procedure).

The game can be diversified by the content of positional cards, which can be set by the students themselves based on the typical problem situations that they face at home and at school.

Game Goals:

Obtaining by schoolchildren the experience of partner behavior in situations with opposing interests of partners;

Development of a positive emotional attitude to the contract as a way of cooperation.

Number of participants: from I2 to 24 people (the number of participants must be a multiple of 3).

Age of participants: 2-11th grade.

Stages of the game

1. Preparatory stage

Purpose: psycho-emotional warm-up, mood for role-playing interaction.

Means: psychological exercises.

Expected result: a positive attitude of the participants towards each other, the removal of emotional and muscular tension, the development of coherence in group actions.

Mini stages:

Acquaintance;

Emancipation of motor activity;

Reincarnation;

Consistency of actions.

2. Main stage

Creation of conditions for partnership interaction of schoolchildren;

Expanding the knowledge of schoolchildren about the ways of cooperation in business communication;

Development of observation and flexibility of behavior.

Means: positional interaction, analysis of positional interaction, presentation of the results of work, handouts for group analysis in the form of observation protocols and positional cards.

Expected result: the experience of business interaction, the experience of observing the conduct of negotiations, the experience of role reincarnation, the expansion of knowledge about the ways of behavior in the negotiation process.

H. Reflective stage

Purpose: awareness by participants of the meaning of the acquired experience, development of a cognitive and positive attitude of participants towards themselves and towards partners.

Means: group and individual reflection of the experience gained.

Expected result: readiness of participants for partnership cooperation, readiness to perceive their classmates as potential partners, desire to learn new ways of cooperation.

4. Diagnostic stage

Purpose: to assess the emotional attitude of schoolchildren to partner interaction and to the form of conducting classes.

Means: visual posters on which the results of an individual assessment are recorded.

Expected result: overall satisfaction of the participants with the game.

PROGRESS OF THE GAME

1. Preparatory stage

The preparatory stage consists of a series of mini-stages that are logically connected and aimed at realizing the goal of this stage.

Acquaintance.

Traditionally, acquaintance is carried out in a circle, where each participant is invited to briefly tell about himself what, in his opinion, few people know. It can be hobbies, interests, occasion and life, etc.

Exercises for the emancipation of motor activity.

The purpose of this stage is to reduce muscle tension, develop friendly, open relationships in the group (class). The main exercises are:

Motor (moving around a chair, catching various “mental objects:“ apples ”,“ bricks ”,“ balloon ”, etc.),

Power (pushing with shoulders, hips, "trying on arm strength," etc.),

Respiratory.

Transformation exercises.

Transformation exercises are aimed at developing children's ability to control their own bodies, to be emotionally open, creative imagination, flexibility behavior.

It is advisable to carry out such exercises in a certain sequence, with complication. For example, the scheme for complicating entering an image can be as follows: Image (“Eagle”) - Image in combination with a property (“Tired Eagle”) - Image in some situation (“Eagle in a cage”) - Complex image.

The most optimal form of organizing this type of exercise is to offer students cards, on one side of which is written the name of the image in which they will have to reincarnate, and on the other - the same image, but complicated by the quality or situation. For example, “Wind2 - “Wind in the desert”, “sofa” - “sofa in a landfill”, “Bear” - “Fed bear”, “Parent” - “Parent after the parent meeting”, etc. As complex images, you can suggest the following: “My father”, “My mother”, “What I want to be”, “How others see me”, etc.

Before proceeding to exercises for coherence of actions, students can be offered to express various emotional states that are recorded on handout cards using gestures and facial expressions: fatigue after class, love for a dog, resentment due to an undeserved assessment, comforting someone, etc.

An effective exercise in this mini-stage is to rehearse the behavior of participants in familiar life situations. For example, students standing in a circle are offered cards that contain actions that need to be performed in relation to a neighbor on the left: draw attention to themselves, make a compliment, ask for something, etc.

Exercises and coherence of actions enable the student to feel like a part of a group, to realize the possibilities of his influence on his comrades, to see the relationship between the success of the group and the personal success of each.

As exercises at this stage, the following can be suggested: tapping or slapping the rhythm in a circle, composing a story in a circle, group drawing, creating a sculpture of a group, etc.

2. Main stage

Before proceeding to the description of the course of the main stage, we will present the forms of the handout of the game.

Protocol.

The number of protocols is equal to the number of participants.

position cards.

The facilitator distributes 2 position cards for each situation (in each microgroup). Each of them contains the name of the position or role of a particular partner and his interest in this situation. Possible examples of position cards are

nones below.

Position cards of situation "A"

Position cards of situation "B"

Positional cards of the situation "G"

The facilitator tells the students about the peculiarities of contractual relations, drawing attention to the main positions that each of the contracting parties must think over in advance for the effective conduct of future negotiations. So, each partner should think about the following questions:

What is my interest (my goal) in negotiations;

What can I "sacrifice" for the sake of concluding a contract;

What I cannot "sacrifice" in the contract under any circumstances;

What is (presumably) my partner's interest in these negotiations;

What (presumably) my partner can "sacrifice" for the sake of the contract;

Something (presumably) my partner will not be able to "sacrifice" under any circumstances.

The facilitator draws the attention of the participants to the variety of forms of behavior of partners in the contract (both verbally and with the help of gestures and facial expressions) and writes down on the board (with commentary) some possible ways of cooperation. This is necessary in order to facilitate the subsequent work of schoolchildren in microgroups.

The following list can be used as a starting point:

Transfer of information

concession,

Help offer,

Clarification of the words and position of the partner,

Belief,

help request,

Bringing arguments

Praise,

Agree with the condition

Help offer,

A pat on the shoulder.

The facilitator invites the students to break into threes, and then sets the goals and positions of the participants in the resulting microgroups.

The purpose of group work for schoolchildren is to strive to agree in the situations proposed by the leader with opposite interests of partners. The attention of schoolchildren should be drawn to the fact that they do not have to agree on the final version within a given time. The main thing is participation in the negotiation process, striving for results.

The positions of the participants of the trio: partner No. 1, partner No. 2, observer.

The task of the partners: to agree in the situation proposed by the presenter on the positional card.

The task of the observer: to complete the observation protocol for partners # 1 and # 2 during the negotiation process in the troika. In the minutes, the observer must first write down (in the first line) the role of each partner specified in the position card and his real name. In the second line of the protocol, the observer writes down the interests of the partners using a position card. The most difficult part of the observer's job is to record in the minutes the ways of behavior that the partners of the trio use in the proposed situation. Of course, observers can use the list of ways to cooperate written on the blackboard. However, they should focus primarily on the ways of behavior actually shown by partners. In order to facilitate the work of observers, the facilitator indicates to the group their rights:

The ability to stop the negotiation process at any time in order to record in the protocol the behavior of partners;

Have your own opinion in interpreting the behavior of partners when filling out the protocol.

The facilitator distributes to each microgroup 3 protocols of observation, as well as a position card (it consists of 2 cards with positions and interests of partners). Examples of position cards are given above. The facilitator sets the time for negotiations and calls a sign (for example, clap) that will signal the participants that their work is over.

The facilitator invites students to choose a position in the negotiation process. After that, each member of the trio takes the appropriate sheet: the observer - the protocol of observation, partner No. 1 and partner No. 2 - their parts of the position card. The leader gives a signal to start negotiations.

After the allotted time, the host records that the negotiations are over and gives observers some time to finalize the protocols.

The facilitator invites the participants to exchange positions within the trio and start negotiating again in the same situation.

Repetition of point number 6.

Repetition of point number 7.

Repetition of point number 6.

The facilitator draws the attention of the participants to the fact that in each triple in this moment are located according to 3 protocols of observation, in which the methods of negotiating by the participants of the troika are recorded. The facilitator gives a task to each microgroup: to analyze all the recorded ways of behavior and write out non-repeating ones from them on a separate sheet. Then a representative from each microgroup reads out the resulting list, and the facilitator writes down the methods on the board, continuing the original list. Of course, the facilitator should not only write down the proposed methods, but also, if necessary, clarify their meaning and reformulate. In the end, you should get such a list of ways to negotiate, which is distinguished by diversity, constructiveness, and effectiveness.

The facilitator suggests that each participant in the game write down the resulting list of negotiating methods in their notebook, and then think and answer the following question: which of these methods are the most effective in concluding an agreement (which of these methods most likely led you to a joint agreement)?

A representative from each microgroup names the most effective methods, expressing the opinion of his trio, and the leader marks these methods in the list (on the board) with some sign: “!”, “+”.

Based on the students' effective ways negotiation, the host sums up the main stage of the game, making a conclusion together with the students about the need to respect the interests of the partner in the negotiation process, compromise as the most important indicator of contractual relations.

3. Reflective stage

At this stage, the facilitator seeks to create conditions for the performance of each participant in the game, whose words should be listened to by the class with understanding and goodwill.

During the discussion, the participants work with the list of methods that they wrote down at the end of the previous stage and with the protocols of observations.

The facilitator proposes the following questions for discussion:

What qualities of a partner have you discovered in yourself?

What qualities of a partner would you like to note in your comrades with whom you agreed?

Which methods from the list do you use most often? Check them off.

Which of the following would you like to learn from the list? Highlight them.

With whom would you like to negotiate now, after mastering some ways of cooperation?

Experience has shown that the reflective stage is more interesting when each member of the trio talks about how his partners have shown themselves in the negotiation process, as well as what they can learn from them.

4. Diagnostic stage

The subject of diagnostics can be the emotional attitude of the participants to the process of their negotiations and to the form of the lesson.

To assess the attitude of schoolchildren to the lesson, you can use an A4 sheet with the following design.

The participants of the game mark their attitude to the lesson in one of the 4 squares by means of any symbols.

The relationship to the contract process can be identified using the following technique. A coordinate system with two scales is drawn on the landscape sheet. The horizontal scale reflects the positions of the participants, the vertical - the points with which each of the participants rated the game. Practice has shown effective 7-point rating scale. This coordinate system might look like this.

Participant numbers

Each participant puts some sign (in this case) in front of the appropriate, in his opinion, the number of points.

If the average score of the emotional attitude to the contract (for the group) exceeds 5 points, then the game can be considered quite effective

Meeting newcomer

This game, like the one described above, is aimed at developing rules of conduct. However, during its implementation, emphasis is placed on visual, imitation methods of participants' work. This is largely determined by the age characteristics of the participants, for whom this game is intended. In this game, the subsequent visual presentation of the results in the form of a wall newspaper, a poster, which demonstrate the effectiveness and usefulness of the game for the life of the class, is very important.

Game Goals:

Development of a positive attitude of schoolchildren to each other;

Development and testing of rules of conduct in relation to new members of the class team;

Development of the ability to cooperate and mutual understanding.

Number of participants: students in the same class.

Age of participants: 2-11th grade.

Stages of the game

1. Warm up

Removal of emotional tension;

Developing the ability to be positively interested in a partner;

Expansion of schoolchildren's ideas about themselves, about comrades, about class life.

Means: psycho-training exercises.

Expected result: creation of a friendly atmosphere in the group and increased interest in further work.

2. Development of rules of conduct in relation to newcomers

Group development of rules for the behavior of schoolchildren in relation to various types of newcomers;

Rehearsal of the developed rules;

Development of group discussion and active listening skills;

Development of flexibility of behavior.

Means: group problem work; "brainstorm" role-playing games; group positional analysis.

Expected Result:

Development of rules for the behavior of schoolchildren towards newcomers in various school situations;

Positive attitude of each to the received list of rules.

Z. Reflexive

Expansion of the image "I am the participants";

Development of willingness to act in accordance with the rules and improve them.

Means: group reflection; designing a visual representation of the resulting rules.

Expected Result:

Willingness to act in accordance with the rules;

Willingness to learn from comrades and teach them to follow the rules through their own behavior;

Improved understanding of self and others;

Development of readiness for cooperation.

Game progress

1. Preparatory stage

The facilitator invites the students to complete the exercise “Honored guest. two participants in the game go out the door. One of them is the guest of honor, the other is the escort, who announces to the participants in the game which guest of honor is in front of them. Four contestants are chosen to form a jury that will evaluate the behavior of the others on a 7-point scale.

The escort brings the guest into the room and introduces them. Then each participant of the game (except the jury) welcomes the guest of honor in turn, says some phrase to him, in general, does everything possible to make the guest feel comfortable. The jury evaluates the behavior of each participant.

2. Main stage

The facilitator invites the students to break up into 3 microgroups.

Each group must develop rules for the behavior of schoolchildren in relation to the character of the new student. The first microgroup develops rules of conduct in relation to the new bully. The second microgroup - in relation to the brand new modest, shy. The third - in relation to the new cheerful and sociable. For ease of registration of the rules, each microgroup is given a form of a table with the following content:

Attitude towards new

In the first line, each microgroup writes down its type of newcomer. Then the possible actions of this newcomer in relation to classmates and teachers are discussed and recorded in the first column. Accordingly, in the second column, such possible reactions of classmates to this behavior are recorded that will help the beginner respect the norms of behavior in the class and more easily fit into the class team. In the third column, the microgroup formulates the rules for the behavior of students in relation to the newcomer based on an analysis of his actions and reactions to them. Thus, the microgroup fills in only the first three columns at this stage. 15-20 minutes are allotted for work.

A representative from each microgroup exposes the completed tables in front of all participants, but their content is not discussed.

The facilitator invites each microgroup to play the actions of their classmates highlighted by it, and the remaining two microgroups must evaluate their reaction from the positive and negative sides (one microgroup evaluates positive sides lost reaction, and another microgroup evaluates the negative aspects). Representatives of the evaluative microgroups name the positive and negative aspects of the scenes they have highlighted, and the moderator writes them down in the fourth and fifth columns of the corresponding tables. After that, the participants, if necessary, correct the original rule, and the facilitator writes it down in the sixth column in the new wording.

The facilitator invites the representative of each microgroup to visualize the rules they have invented and hang them in the office.

3. Reflective stage

The facilitator suggests telling the participants of the game about whether they had to be new in the class or group? How were they met? How would they like to be greeted? What was the hardest thing to adjust to? What lessons have been learned from this situation?

in the case of a new student coming to the class, draw up a poster on which his photograph is pasted and the rules for treating the new student on the part of classmates are written out from the list of those developed during the game.

Choice of the parent committee of the class

The presented game allows the class teacher to create

an effective parent committee interested in the joint conduct of educational affairs.

Game Goals:

Drawing up a list of joint educational affairs with parents;

Election of the parent committee of the class.

Number of participants: corresponds to the number of parents

in class.

Stages of the game

1. Preparatory stage

Acquaintance of parents;

Identification of parents' expectations regarding educational work in the classroom;

Drawing up a list of areas of joint work of parents and students for a certain period of time (six months, a year).

Means: psycho-training exercise, group problem work.

Expected result: a list of areas of joint educational affairs in which the parents themselves are interested; positive attitude of parents towards each other; determination of the possibilities and desires of each parent to participate in the educational work of the class and school.

2. Main stage

Finding out the possibilities and interest of participants in relation to

to the allocated educational directions and affairs;

Creation of temporary interest groups of parents in educational affairs;

Distribution of functions for the effective implementation of educational work;

selection of a representative to the parent committee as a leader from the group of parents.

Means: group analysis, group evaluation. Expected Result:

Formation of teams of parents interested in educational affairs of a certain type;

Allocation of leaders in groups of parents;

Choice of parent committee.

H. Reflective stage

Purpose: to analyze the satisfaction of participants from participation in a particular case.

Means: individual-group reflection.

Expected result: satisfaction with the results of the game.

Game progress

1. Preparatory stage

Parents sit in a circle. The facilitator invites each parent to introduce themselves in turn, and then answer two questions.

What, in your opinion, is the role of parents in the organization of educational work in the classroom?

How can you help the class teacher in organizing educational work in the classroom?

The facilitator invites parents to break into microgroups of 4-5 people each and gives them a task: during the discussion, each microgroup should highlight the main areas of work for the future parent committee. 12-15 minutes are given for work.

A representative from each group names the directions received, and the facilitator writes them down on the board, clarifying the meaning of each and not writing down the repetitive ones. As a result, the main directions of work of the future parent committee are fixed on the board. You can present them in the form of a table (the first column is filled).

2. Main stage

The facilitator puts a sign with the name of the direction of work in each microgroup. Then he invites those parents who can be useful to the class within this direction and show interest in it to unite in one microgroup.

Each newly created microgroup leader gives the task: 1

through a group discussion, come up with 1-2 joint cases within the given direction (parents + schoolchildren + class teacher).

Then the parents, having discussed in a microgroup their possibilities in organizing the proposed cases, distribute the functions within each case (negotiate with someone, arrange something, find, conduct, etc.). At the same time, a coordinator is selected in each case, who is primarily responsible for the implementation of the case and maintains communication between the team and the class teacher.

A representative from each microgroup reads out the resulting cases, and the facilitator writes them down in the previously proposed table in the second column. In addition, the name of the responsible person, that is, the coordinator elected in the microgroup, is recorded in the table (third column).

The facilitator, recorded in the table the names of all the coordinators, asks them to leave and invites them to become members of the parent committee, because it was the parents themselves who showed the greatest confidence in them regarding class affairs. If the coordinator does not agree to become a member of the parent committee, then the microgroup must propose a replacement.

H. Reflective stage

Parents, being in a circle, express their attitude to such a practice of elections. Members of the microgroup name those qualities of coordinators and elected members of the parent committee, thanks to which the trust of the microgroup was expressed to them.

After the game, the coordinators, together with the class teacher, discuss the content and distribution of powers in the proposed joint cases (this was done in microgroups during the game), and then outline the sequence of implementation

educational affairs.

Reflective game

Reflective game- process social interaction, during which each of the participants in the game exercises reflexive control (the author of the term is V. A. Lefebvre) by other participants, trying to implement the management strategy he has to form his own version of social reality (implementation of a social innovation project). In the space of a reflexive game, social management technologies are tested for effectiveness, so the gain in such a game is an increase in the level of skill.

Reflective play as a type of social interaction

Reflexive play refers to open type games. Unlike games that proceed according to a script and according to predetermined rules (such as business games or role-playing games), reflective games are a process of social interaction in which roles, rules and plot moves are generated by participants right along the way. game action. At the same time, the course of the reflexive game can be controlled using the individual personal characteristics of the participants, the configuration of their business and personal interests, preferences, expectations, goals, fears and temptations.

In a reflexive game, the advantage is given to the one who is more equipped with the tools to manage people and social processes, the one who is more sophisticated in analyzing and calculating situations of social interaction. Of all the existing variants of reflexive games, the most famous are ODI (organizational-activity games), first used to solve social problems by G. P. Shchedrovitsky. However, there are other varieties of reflexive games developed by students, followers and even ardent opponents of G. P. Shchedrovitsky.

Typology of reflexive games

Every reflective game has task or set of tasks which it must solve by the participants. According to the tasks solved in the course of reflexive games, they can be divided into two types.

To first type include reflexive games, the main task of which is to create conditions for the individual development of participants. Reflexive games of the first type can be used for professional training or retraining of participants who are not elements of any one social system. Reflexive games of the first type can be used to identify and develop cultural and mythological stereotypes and attitudes that are characteristic of the participants. They can also be used to form megamachines (social systems made up of elements and parts of other social systems) - for example, during political campaigns or nationwide (or interstate) projects, the implementation of which involves the capabilities of a large number of different social systems.

Co. second type include reflexive games, the main task of which is to generate social innovation that will change the social system, the elements of which are the subjects-participants. Such games can be used to implement such specific activities for the development of social systems as management consulting.

Reflective Game Project

Reflexive games of the first and second types are conducted under the control of a team of game technicians who ensure such a flow. gameplay, during which the tasks assigned to the game are solved. To conduct a reflexive game (of the first or second type), a team of game technicians needs game project. The project is created by a team of game engineers under the guidance of methodologists. (A methodologist is a thinker who is able to develop new approaches to the design of reflexive games, using the apparatus of methodological thinking for this (see SMD methodology)). The process of generating a game project can be called a metagame, which is carried out by methodologists with a team of game technicians on the eve of a reflexive game. In the course of game design, a team of game technicians carefully works out diagnostic information (information about the participants and about the social system (systems), the elements of which are the subjects-participants), detail the topics and meanings around which the discussion will be built within the groups and during the game, determine the best for solving this problem is a way to divide players into groups and calculate the dynamics of intragroup and intergroup gaming interaction.

Organizational structure of reflexive play

Reflexive games of the first and second types can proceed only under the condition that a rigid organizational structure of the game(dividing the participants into groups, each of which is assigned at least one game technician, determining the time schedule game events, definitions of forms of intra-group and general game communication and rigid rationing communication). The structure of the game is a meta-norm that is held by the team of game technicians in relation to the players. Players have a lot of freedom, however, this freedom is limited by clearly defined limits, for example: players cannot move from group to group, the group cannot exceed the time allotted for the report during the general game meeting, the group must clearly state the topic of the report and not deviate from it, you can ask questions for understanding to the report, but you can’t mix them with judgments about what you heard in the report, you can’t ask questions about what was not in the report, etc. The norms, rules and elements of the organizational structure of the reflexive game may vary depending on on the preferences and methods used by the gaming team and methodologists conducting the game.

Rationing of players' actions, self-reflection and reflexive state

There are quite a lot of norms that hold the structure of the game, and the team of game engineers can invent them in the course of the game action. Basic normative questions: “What are you doing now?” or “What is the meaning of your action here and now?” are uncomfortable enough to draw the speaker's or the group's attention to their own thinking process, thus putting them in a self-reflexive position. When a player learns, while maintaining an autoreflexive position, to set goals, design and implement actions and analyze the result of the actions taken, he passes into a reflective state and acquires a new degree of intellectual and creative freedom, since from a reflective state he is able to work with the meanings of his own and other people's actions and to carry out reflexive management actions, the effectiveness of which is significantly higher than that of actions carried out not from a reflexive state.

There are several levels of the reflective state (“reflexive levels” or “reflexive layers”). The more reflexive levels a player is able to build on (the higher his reflexive potential), the more opportunities he gains in designing social innovations, in managing people and social processes, and in calculating social situations. A subject with a higher reflexive potential has a significant advantage over a subject whose reflexive potential is lower.

Thus, the reflexive game does not in any way impose topics or options for self-determination on the players, but it creates for each player a unique chance to expand their thinking and increase their reflexive potential.

Literature

• S.A. Kutolin"Reflexive Literature"
• S.A. Kutolin"Literature as illumination by reflection"
• Lefevre V. A. conflicting structures. M.: Soviet radio, 1973;
• Novikov D. A., Chkhartishvili A. G. Reflexive games. - M.: Sinteg, 2003.
• Makarevich V. N. Game practices, methodologists: the invisible community "comes out of the underground.//Sotsis, 1992, N 7;
• Kotlyarevsky Yu. L., Shantser A. S. The art of modeling and the nature of play. M., Progress, 1992. - 104 p.;
• Shchedrovitsky G.P. Selected works. M., Shk. Cult. Polit., 1995.

see also

Links

• Shokhov A. S. Method of live modeling in the study and consulting of organizations

Wikimedia Foundation. 2010 .

See what "Reflexive game" is in other dictionaries:

Game - get a valid promotional code MIF publishing house at Academician or buy a profitable game at a discount on sale at MIF publishing house

A business game is a method of simulating decision-making by executives or specialists in various production situations, carried out according to given rules by a group of people or a person with a PC in an interactive mode, in the presence of conflicts ... ... Wikipedia

The gaming (gaming) community, which originally arose in the USSR and now exists in Russia and Belarus, is a large group of specialists practicing the use of games, gaming methods in various areas of public life: in the economy, ... ... Wikipedia

A business game is a method of simulating decision-making by executives or specialists in various production situations, carried out according to given rules by a group of people or a person with a computer in an interactive mode, in the presence of conflicts ... ... Wikipedia

- (English practice firm, fictitious firm) an active form of training schoolchildren, students and trainees of practical activities at the enterprise. A training company is created on the basis of a school, primary vocational, secondary specialized or higher ... ... Wikipedia

Activities aimed at improving the efficiency of firms, companies, organizations. Contents 1 Types of management consulting 1.1 Strategic consulting ... Wikipedia

- "Reflexive processes and management" international scientific and practical interdisciplinary journal. Founders: Institute of Psychology of the Russian Academy of Sciences and Lepsky Vladimir Evgenievich, with the participation of the Institute of Reflective Processes and Control Since 2001, 2 have been published ... ... Wikipedia