Reflexive Games Research Articles

Heuristic modeling of reflection in reflexive games

The functioning of a subject in a changing environment is most effective from the point of view of survival if the subject can form, maintain and use internal representations of the external world for decision-making. These representations are also called reflection in a broad sense. Using it, one can win in reflexive games since an internal representation of the enemy allows predicting their future moves. The goal is to assess the reflexive potential of heuristic model objects – artificial neural networks – in the reflexive games “Even-Odd” (or “Matching pennies”) and “Rock-Paper-Scissors”. We used homogeneous fully connected neural networks of small sizes (from 8 to 45 neurons). Games were played between neural networks with different configurations and parameters (size, step size for modifying weight coefficients). A set of reflexivity criteria is presented, corresponding to different levels of consideration: neuronal, behavioral, formal. The transitivity of formal success in the game is shown. The most successful configurations, however, may not meet other criteria of reflexivity. We hypothesize that the best compliance with the criteria and, as a consequence, universal success in reflection tasks is achievable for heterogeneous configurations with a structure in which the formation of hierarchical systems of attractors is possible.

Jeux réflexifs et procédés métafictionnels dans Kétala de Fatou Diome

Cet article ambitionne à relever les procédés métafictionnels qui impliquent une narration introvertie dans le roman Kétala de l’écrivaine africaine Fatou Diome. Il s’attache aussi à dépister leurs renvois en essayant, toutefois, de relier la performance textuelle de l’auteure à son expérience personnelle, pour voir l’investissement des jeux réflexifs que Diome relie à un véritable travail narratif, qu’elle appelle : le mot-motage.

Solving the Cournot Oligopoly Game under Incomplete Information with the Possibility of Cooperative Interaction

The balance of commodity markets is an extremely important and pressing challenge. There is an active development of research aimed at solving such problem. However, well-known theoretical models do not always adequately reflect the desire of agents to make such individual decisions and search for such compromises to ensure the greatest profit and bring the market to equilibrium.
 The article considers the solution of the Cournot oligopoly game under incomplete information for the case of linear demand and linear costs. The approaches of the reflexive games theory and collective behavior theory are the basis for the construction of the decision-making process by agents. The policy of optimal responses of agents to the expected output volumes of the environment under traditional assumptions about the independence of agents may not lead to equilibrium. Therefore, the article considers and proposes non-traditional solutions that allow agents to cooperate. It is shown that it is enough to jointly regulate the process only at initial stage. After that, it should come to equilibrium if, in the future, agents independently adjust their own output, counting on the maximum expected profit. The necessary assertions and their mathematical proofs are given.

Modeling the Dynamics of Collective Behavior in a Reflexive Game with an Arbitrary Number of Leaders

An oligopoly with an arbitrary number of Stackelberg leaders under incomplete, asymmetrical agents' awareness and inadequacy of their predictions of competitors' actions is considered. Models of individual decision-making processes by agents are studied. The reflexive games theory and collective behavior theory are the theoretical basis for construction and analytical study process models. They complement each other in that reflexive games allow using the collective behavior procedures and the results of agents' reflections, leading to a Nash equilibrium. The dynamic decision-making process considered repeated static games on a range of agents' feasible responses to the expected actions of the environment, considering current economic restrictions and competitiveness in each game. Each reflexive agent in each game calculates its current goal position and changes its state, taking steps towards the current position of the goal to obtain positive profit or minimize losses. Sufficient conditions for the convergence of processes in discrete time for the case of linear costs of agents and linear demand is the main result of this work. New analytical expressions for the agents' current steps' ranges guarantee the convergence of the collective behavior models to static Nash equilibrium is obtained. That allows each agent to maximize their profit, assuming common knowledge among the agents. The processes when the agent chooses their best response are also analyzed. The latter may not give converging trajectories. The case of the duopoly in comparison with modern results is discussed in detail. Necessary mathematical lemmas, statements, and their proofs are presented.

Пандемия и спецоперация: многодисциплинарный анализ с использованием подхода "4К"

Using the author's ”4C” approach, two global processes are considered, apandemic and a special military operation that significantly affect the Russian Federation. The low effectiveness of science in understanding these processes is noted. The potential of the theory of reflexive control V.A. Lefebvre is discussed. Variants ofdevelopment of methods of the reflexive games theory are offered. The author's options for analyzing and forecasting situations offered in 2013 and 2020 are discussed. Options for forecasting the development of the situations are proposed.

Design features of the synthetic learning environment

The article considers the features of the learning transformation in the transition from the usual material-object environment to learning in the digital synthetic environment. Attention is drawn to the fact that nowadays’ students prefer online and blended learning, in which human interaction with technical learning tools not only creates new opportunities, but also requires coordination of their interaction. A brief description of the main features of learning using new technological capabilities is given, highlighting such aspects as virtual and augmented reality, as well as the use of game-oriented technologies with an emphasis on reflexive games. An analysis was made of changes in the properties of a new learning environment from the standpoint of biotechtonics, which develops the principles of accounting the human factor, i.e. the coordination of human capabilities with technical systems in a digital learning environment in which a person is transferred to a new interactive space using devices that reflect signals in his/her sensory organs and devices, accepting different actions. Variants of teaching technologies based on new principles are proposed, which make it possible to improve the quality of assimilation of educational material. It is noted that the basis for creating complex synthetic learning environments are biotechnical systems, which provide a variety of image content management tools for models of these environments, both for the researcher and the student. It is proposed to expand the concept of ``biotechnical system'' by including the so-called ``biotechnical technologies'', which becomes especially relevant in the digital world. The difference between this type of technology lies in the fact that among the technological operations included in them, great importance should be given to operations that are associated with ensuring the safety of work and creating optimal conditions for the resilience and labor activity of a person. At the same time, a person interacts mainly with information technologies, with information and knowledge that affect him/her, but not with material objects, both in the process of management and in the process of studying the outside world to use it effectively.

Reflective Doctrine Analysis and Impact on the Internal and Foreign Policy of the Republic of Moldova

In this article, I aim to highlight the importance of the analysis on the impact of reflexive gameson the internal and foreign policy of the Republic of Moldova. Such analyzes are applied for the first time in our country regarding reflexive games. Until now, Moldova has been the subject and object of external reflexive applications. Advances in information technology are less visible and palpable for the reading public, which is not only a consumer of information, but also a subject and object of reflective informal technologies. Mathematics specialists model and create effective quantitative conflict management models. Experts in game theory and decision-making promote their own approaches in an increasingly wide range of fields (political, military, economic, etc.). But at the same time, the same specialists say that the individual is described too simplistically, the large sets and masses, with their properties, do not fit into mathematical models. One of the radical challenges for game theory and decision-making theory remains the need to develop the apparatus of reflection (first conceptually, then formally). Reflexive analysis refers to one’s own awareness of the meaning of reflexive communication and interpersonal interaction. At the same time, the reflection as an object of research, since the introduction of this category by J. Locke, is considered entirely belonging to the fields: philosophy and psychology.

Comparative Analysis of Iterative Processes of Equilibrium Calculation in Oligopoly Models

The problem of choosing the optimal behavior of agents in the classic one-product model of the competitive market under linear functions of demand and costs of agents is considered. The dynamic decision-making processes under conditions of uncertainty of decision making by competitors, performed as repeatable static games within a range of admissible answers, are investigated. The analysis targets processes with rational agents using approaches of multi-step reflexive games and models of collective behavior to refine the solutions while observing the current market prices of goods. The processes are distinguished by choosing the current targets: in one case, the agents choose their current output as the current targets when refining the solutions; in another case, the current targets are perceptions of agents about the current equilibrium marginal cost of other agents. It is shown that for oligopolies with Cournot and/ or Stackelberg competition, processes with agents focused on the expected optimum output are more preferable than processes with agents focused on their perceptions of the equilibrium marginal costs of competitors because there are greater opportunities for finding equilibrium states.

Perfect Strategies for Non-Local Games

We unify and consolidate various results about non-signall-ing games, a subclass of non-local two-player one-round games, by introducing and studying several new families of games and establishing general theorems about them, which extend a number of known facts in a variety of special cases. Among these families are {\it reflexive games,} which are characterised as the hardest non-signalling games that can be won using a given set of strategies. We introduce {\it imitation games,} in which the players display linked behaviour, and which contains as subclasses the classes of variable assignment games, binary constraint system games, synchronous games, many games based on graphs, and {\it unique} games. We associate a C*-algebra $C^*(\mathcal{G})$ to any imitation game $\mathcal{G}$, and show that the existence of perfect quantum commuting (resp.\ quantum, local) strategies of $\mathcal{G}$ can be characterised in terms of properties of this C*-algebra, extending known results about synchronous games. We single out a subclass of imitation games, which we call {\it mirror games,} and provide a characterisation of their quantum commuting strategies that has an algebraic flavour, showing in addition that their approximately quantum perfect strategies arise from amenable traces on the encoding C*-algebra. We describe the main classes of non-signalling correlations in terms of states on operator system tensor products.

Equilibria in the Stackelberg Oligopoly Reflexive Games with Different Marginal Costs of Agents

This paper considers the problem of searching for information equilibria in an oligopoly market in the case of Stackelberg leaders. A framework considers the reflexive behavior of three agents, and linear agent’s cost functions with different coefficients (i.e., marginal and fixed costs) are considered. The results of the study are as follows. First, models of the reflexive games for a triopoly that consider a diversity of agents’ reasonings about environmental strategies are developed. Second, formulas for calculating equilibria in the games with three agents for arbitrary reflexion rank are derived.

Neural networks playing ‘matching pennies’ with each other: reproducibility of game dynamics

Reflection is an essential feature of consciousness and possibly the single most important one. This fact allows us to simplify the objective of the concept of ‘neural correlates of consciousness’ and to focus investigations on reflection itself. Reflexive games are the concentrated and pure embodiment of reflection manifestation without the addition of other higher cognitive functions. In this paper, we use the game ‘matching pennies’ (“Odd-Even”) in order to trace the strategies and possible patterns of recurrent neural network operation. Experimental results show the splitting of all considered game patterns into two groups. A significant difference was observed in these groups of patterns, indicating a qualitative difference in game dynamics apparently due to the qualitatively different dynamic patterns of neuron excitations of the networks. A similar splitting of all players into two groups was found by other authors for human players, which differ in terms of the reflection availability. By this, we can assume that one of the causes of the splitting is that the presence of reflection in a particular group of recurrent neural networks dramatically changes the game meta-strategy.

Equilibria in the Stackelberg Oligopoly Reflexive Games with Different Marginal Costs of Agents

Equilibria in the Stackelberg Oligopoly Reflexive Games with Different Marginal Costs of Agents

СИНТЕТИЧЕСКАЯ ОБУЧАЮЩАЯ СРЕДА: ОСОБЕННОСТИ ПРОЕКТИРОВАНИЯ

The article discusses the transformation of teaching in the transition from traditional material-object environment to learning in a digital synthetic environment. Attention is paid to the fact that, to date, students prefer online and mixed learning, in which human interaction with technical training tools creates not only new opportunities, but also requires the coordination of their interaction. A brief description of the main features of training usage of new technological capabilities is given, with emphasis on such aspects as virtual and augmented reality, as well as the use of game-oriented technologies with an emphasis on reflexive games. The analysis of the changes in the properties of the new learning environment is given from the standpoint of biotechnology, developing the principles of harmonizing human capabilities with technical systems (accounting for the human factor) in a digital learning environment, in which a person is transferred to a new interactive space using devices that reflect signals in his/her sensory organs, and devices that perceive different actions. The variants of teaching technologies on new principles are offered, which allow improving the quality of mastering the educational material. It is noted that the basis for the creation of complex synthetic learning environments are biotechnical systems, which a variety of means for controlling the content of images for the models of these environments are provided in, both by a researcher and a student. It is proposed to extend the concept of "biotechnical system" by including so-called "biotechnical technologies" in it, which becomes especially relevant in the digital world. The difference between these types of technologies is in the fact that great importance should be given to operations that are associated with ensuring the safety of work and creating optimal conditions for the life and work of a person. At the same time, the person interacts primarily with information technologies, with information and knowledge affecting him, but not with material objects, in both the process of management, and the process of studying the outside world for the purpose of its effective use.

Crisis consultations as a component of political management

It is determined that crisis consultations represent a set of measures aimed at stabilizing the situation of a particular subject, solving a set of problems associated with the maximum increase in the efficiency of the activity. The following types of crisis consultations are singled out: direct consultations of managers; implementation of advisory activities (consultations on emerging problems, diagnosis of the organization, definition of a crisis strategy, development of a plan of measures for crisis prevention, risk assessment and follow-up of its implementation, support of the organization during the implementation of the plan for crisis prevention, development of preventive measures in relation to avoidance of crisis phenomena); crisis reflexive games (training of managers and staff); case study review; use of benchmarking methods. The role of crisis analysis in conducting crisis consultations has been determined. It was emphasized that crisis analysis enables to prevent and plan possible crisis situations, ways of their neutralization and overcoming with minimal expenses for the organization. The role functions of crisis advisers are determined. The stages of crisis management (according to R. Heath) are revealed: prevention – prevention of crisis risks, analysis of losses for business; readiness – awareness of the probability of crises, staff training; salvation – drawing up plans, preventing consequences; recovery – recovery of effective production, assessment of the crisis. The types of crisis management are distinguished: preventive, aimed at analyzing the indicators of the crisis and identifying its causes and factors for timely prevention or minimization of possible crisis processes; an anticipatory, the essence of which is to develop goals and objectives for leadership in order to prevent crisis phenomena. A demarcation of crisis management and risk management has been conducted: if crisis management is primarily a process of responding to already existing serious threats to one or another organization or to events that have already occurred, risk management is associated with the process of identifying certain risks mainly for future activities organization, as well as the appropriate acceptance of these risks or their elimination.

Modeling of inner currency in reflexive games with multi-criteria payoff functions

The problem of decision-making under conditions of the conflict, multi-objective uncertainty and reflexive interaction of the parties is considered. Modeling of reflexive behavior makes it possible to analyze situations when the decisions taken differ from the non-reflexive rationality, to investigate and reveal the internal causes for such behavior. The solution of this problem, taking into account the multi-valued interests of the parties, is based on a multi-criteria generalization of the proposed V. Lefebvre setting, based on the use of the concept of inner currency. To calculate the initial assessment of the opponent's inner currency on the basis of nominally known criteria, the interval estimates method was used. Its application enables experts to set a range of possible values of weight coefficients, without requiring the definition of their specific values, which simplifies the expert procedure. The further refinement of the weighting factors occurs by solving an auxiliary problem for finding corrections that are introduced into the model for determining the inner currency.

Reflexive Games in Management

Abstract In this paper reflexive games are defined as a way to act beyond equilibria to control our opponents by our hiding motives. The task of a reflexive game is to have the opponent’s actions become transparent for us, while our actions remain obscure for the competitor. In case a reflexive game is carried out between agents belonging to the same organisation (corporation, company, institute), success in a reflexive game can be reached by a purposeful modification of some components of a controlled system. Such a modification for the guaranteed victory in a reflexive game is called reflexive management. This kind of management uses reflexive games to control a knowledge structure of agents in a way their actions unconsciously satisfy the centre’s goals.

Конструктор моделей субъектов рефлексивных игр: версия 1

The constructor of subjects of reflexive games is considered as a component of reflexive control support in the project "Gen-Guru". The project is implemented using cross-technologies of the situational center. The key ideas of the system of models of V.A. Lefebvre are analyzed. The variants of detailing the models for increasing the accuracy of modeling situations are listed. The specifics of modeling such subjects as individuals and robots are considered.

Game-theoretic analysis of Stackelberg oligopoly with arbitrary rank reflexive behavior of agents

PurposeThis paper aims to consider the problem of determining the equilibriums on oligopoly market in case of Stackelberg leader (leaders) and reflexive behavior of market agents.Design/methodology/approachThis paper includes economic and mathematical modeling, optimization methods and game theory.FindingsThis paper explains models of reflexive games on oligopoly market, taking into account the diversity of agents’ reasoning about strategies of environing and equilibrium mechanisms for coincidence or opposition of agents’ reflexive reasoning on the same rank of reflection.Research limitations/implicationsThis paper considers the oligopoly market with linear function of demand and costs of agents, the rational behavior of agents and the reflexive reasoning on the same rank of reflection. The set of agents’ reasoning about the environing strategies is considered as a set of market states for which the problem of agent’s optimal action choosing solves with the complete awareness.Practical implicationsIdentification of reflexive behavior of environing allows agents to increase their market shares and profit.Social implicationsOligopoly markets play a leading role in the world oil trade and reflexive behavior affects the market equilibrium.Originality/valueIn the paper, the mechanisms of equilibrium in reflexive games on the linear duopoly market for arbitrary rank reflection are developed.

Неравновесие по Штакельбергу и динамика коллективного поведения

In this paper, an oligopolistic market of Stackelberg firms only is considered. The problem of achieving the Stackelberg disequilibrium using reflexive games and models of collective behavior dynamics is investigated in the class of demand and cost linear functions for oligopolistic firms. The problem peculiarity is the behavior of oligopolists that comes from incorrect (iteratively adjustable) ideas of marginal costs of other oligopolists while evaluating the scope of delivery. The model of indicator (collective) behavior is the basis of dynamic procedure of clarifying the ideas of marginal costs. The necessary and sufficient conditions for the convergence regardless of initial ideas, the dynamic procedure with constant and equal steps to the Stackelberg disequilibrium with true values of marginal costs of oligopolists for all firms are obtained. The presented results demonstrate the possibility of correct evaluation of certain characteristics of competitors for markets based on incorrect ideas of oligopolists on a behavior of competitors.

Graph of a Reflexive Game and Bélles-léttres

Abstract The authors consider reflexive games that describe the interaction of subjects (agents) making decisions based on an awareness structure, i.e., a hierarchy of beliefs about essential parameters, beliefs about beliefs, and so on. It was shown that the language of graphs of reflexive games represents a convenient uniform description method for reflexion effects in bélles-léttres.