Game theory and its economic applications
Abstract
The manual describes the main sections of game theory, the basic concepts of the theory of economic risks and the conceptual framework for modeling the process of making managerial decisions in the economy based on the combined application of statistical and antagonistic games. Antagonistic games (AG) are the finite games of two persons with zero sum, i.e. matrix games, with classical antagonistic games called AG, given by completely known matrices, and neoclassical antagonistic games – AG, given by partially known matrices. The manual is intended primarily for masters who study in the direction of training "business information". However, it will be useful for students and postgraduates studying in large groups of areas of training "Economics and Management", "Mathematics and Mechanics", "Management in Technical Systems", as well as scientific and pedagogical workers specializing in the field of the theory of games, risk managers , managers and economists-practitioners.
... Many experiments have shown that such a behaviour, or some approximation of it, is widespread among human and animal actors. Interestingly, this crudest form of a learning rule works even in situations involving several agents, as in the so-called minimal social situation (Colman 1995). ...
... We are interested in exploring how adaptation works when playing against other players. In the repeated prisoner's dilemma game, for instance, a strategy called PAVLOV does very well (see Kelley et al. 1962;Colman 1995;Kraines & Kraines 1988;Nowak & Sigmund 1993). PAVLOV is a win^stay, lose^shift rule with an aspiration level lying somewhere between the two highest and the two lowest pay-o¡s. ...
... There are then 12 di¡erent rank orderings. They correspond to very di¡erent strategic situations (see for example, Rapoport et al. 1976;Binmore 1992;Colman 1995). It is no restriction of generality to assume R4P (if this does not hold, we just interchange C and D) and to normalize the values such that R 1 and P 0. Each game, then, corresponds to a point in the (S,T)plane, and the 12 rank orderings correspond to 12 planar regions (see ¢gure 1). ...
Win-stay, lose-shift strategies in repeated games are based on an aspiration level. A move is repeated if and only if the outcome, in the previous round, was satisficing in the sense that the payoff was at least as high as the aspiration level. We investigate the conditions under which adaptive mechanisms acting on the aspiration level (selection, for instance, or learning) can lead to an efficient outcome; in other words, when can satisficing become optimising? Analytic results for 2×2-games are presented. They suggest that in a large variety of social interactions, self-centered rules (based uniquely on one's own payoff) cannot suffice.
... Obviously, to evaluate the efficiency of different forms of conducting classes we should use different methods of mathematical modeling and, in particular, game-theoretic models of different classes. We believe that it is possible to use antagonistic (matrix) games to assess the efficiency of the traditional form of conducting classes (see, for example, [19]). However, to assess the efficiency of the interactive form of conducting classes, the use of antagonistic (matrix) games is not possible. ...
... However, to assess the efficiency of the interactive form of conducting classes, the use of antagonistic (matrix) games is not possible. To assess the efficiency of the interactive form of conducting classes, it seems appropriate to use cooperative games (see, for example, [19]). Let us examine in more detail the simplest game-theoretic model for evaluating the efficiency of the traditional form of conducting classes. ...
Today, there is an urgent need to use distance technologies in education. The significant disadvantages of e-learning are students’ low self-motivation, and the insufficient level of formed social communication skills. The above disadvantages can be largely overcome with interactive teaching methods and appropriate information technologies in the educational process. A correct approach in including interactive technologies in e-learning provides significant positive effects. One of the main challenges in using interactive technologies in e-learning is how to organize efficient remote dialogue and joint work of the participants. The paper analyzes information technologies recommended at various stages of organizing and designing interactive learning technologies. When working in groups, students can use online services such as Google Sheets, Google Docs, and Google Slides. These services greatly facilitate the work on a joint project and help the project team prepare for its successful presentation. Since many e-learning platforms cannot provide high-quality communication for participants, video conferencing services and social networks should supplement them. E-learning platforms should ensure that learners work effectively on common tasks using interactive learning technologies. We believe that every modern e-learning platform should contain a software module similar in functionality to Google Docs, Google Sheets, and Google Slides. It will make it possible to successfully implement all stages of organizing and designing interactive learning technologies. We can evaluate the efficiency of the forms of conducting classes using mathematical modeling, in particular, game-theoretic modeling. To assess the efficiency of the traditional and interactive forms of conducting classes, it is advisable to use an antagonistic (matrix) game and a cooperative game, correspondingly.
... Cooperative behavior is ubiquitous in the real world and can be found both in natural and social systems [1] . Understanding the emergence and maintenance of cooperation among selfish individuals has drawn considerable attention from researchers across many different fields in the past decades. ...
... According to the Darwinian evolutionary theory [2], any behavior that contributes benefits to others but not directly to oneself will soon disappear. However, this is not fully consistent with the ubiquitous existence of cooperative behaviors in uncountable biological or social settings, especially in animal and human societies [3][4][5][6]. In order to solve this puzzle, a variety of game theoretical models inspired by different biological situations, such as the prisoner's dilemma game, the snowdrift game and public goods games, have been extensively studied [7][8][9][10][11][12][13][14][15][16][17][18]. ...
In realistic world individuals with high reputation are more likely to influence the collective behaviors. Due to the cost and error of information dissemination, however, it is unreasonable to assign each individual with a complete cognitive power, which means that not everyone can accurately realize others' reputation situation. Here we introduce the mechanism of inferring reputation into the selection of potential strategy sources to explore the evolution of cooperation. Before the game each player is assigned with a randomly distributed parameter p denoting his ability to infer the reputation of others. The parameter p of each individual is kept constant during the game. The value of p indicates that the neighbor possessing highest reputation is chosen with the probability p and randomly choosing an opponent is left with the probability 1-p. We find that this novel mechanism can be seen as an universally applicable promoter of cooperation, which works on various interaction networks and in different types of evolutionary game. Of particular interest is the fact that, in the early stages of evolutionary process, cooperators with high reputation who are easily regarded as the potential strategy donors can quickly lead to the formation of extremely robust clusters of cooperators that are impervious to defector attacks. These clusters eventually help cooperators reach their undisputed dominance, which transcends what can be warranted by the spatial reciprocity alone. Moreover, we provide complete phase diagrams to depict the impact of uncertainty in strategy adoptions and conclude that the effective interaction topology structure may be altered under such a mechanism. When the estimation of reputation is extended, we also show that the moderate value of evaluation factor enables cooperation to thrive best. We thus present a viable method of understanding the ubiquitous cooperative behaviors in nature and hope that it will inspire further studies to resolve social dilemmas.
... According to the principles of Darwinian selection, any behavior that brings benefits to others but not directly to oneself will soon disappear (Darwin, 1958). However, this is not fully consistent with observations that attest to the existence of cooperative behavior, with examples ranging from the communities of microorganisms to animal and human societies (Milinski, 1987;Binmore, 1994;Colman, 1995;Doebeli and Hauert, 2005). In order to explain the emergence and maintenance of cooperation, evolutionary games, with the focus on social dilemmas, have provided several fundamental insights (Hofbauer and Sigmund, 1998;Ren et al., 2006;. ...
In spatial evolutionary games the fitness of each individual is traditionally determined by the payoffs it obtains upon playing the game with its neighbors. Since defection yields the highest individual benefits, the outlook for cooperators is gloomy. While network reciprocity promotes collaborative efforts, chances of averting the impending social decline are slim if the temptation to defect is strong. It is, therefore, of interest to identify viable mechanisms that provide additional support for the evolution of cooperation. Inspired by the fact that the environment may be just as important as inheritance for individual development, we introduce a simple switch that allows a player to either keep its original payoff or use the average payoff of all its neighbors. Depending on which payoff is higher, the influence of either option can be tuned by means of a single parameter. We show that, in general, taking into account the environment promotes cooperation. Yet coveting the fitness of one's neighbors too strongly is not optimal. In fact, cooperation thrives best only if the influence of payoffs obtained in the traditional way is equal to that of the average payoff of the neighborhood. We present results for the prisoner's dilemma and the snowdrift game, for different levels of uncertainty governing the strategy adoption process, and for different neighborhood sizes. Our approach outlines a viable route to increased levels of cooperative behavior in structured populations, but one that requires a thoughtful implementation.
... Other aspiration levels, with or without averaging, define other variants of the Win-Stay-Lose-Shift class of (meta-)strategies. The set of these rules can be extended by allowing a dynamic change of the aspiration level, as it appears frequently in human and animal examples (Colman, 1995). These strategies involve a way how the aspiration level changes step by step knowing the previous payoffs. ...
Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games. Comment: Review, final version, 133 pages, 65 figures
The article focuses on the problem of choosing the optimal strategy for the development of the system of Internet order pick–up points in the context of the dynamics of solvent demand and competition of Internet stores for the market of consumer goods. A game model of the situation of choosing a strategy for the development of a system of base-level delivery points is constructed, which allows quantifying the usefulness of each of the strategies in accordance with the possible values of the number of orders and the value of the average check. From a mathematical point of view, the constructed game model belongs to the class of games with a generalized player «Nature». A study of the game model of choosing a strategy for the development of the system of order pick-up points of Internet stores based on the use of several criteria used in information situations of complete uncertainty. The obtained results of game modeling have received a meaningful interpretation in terms of the economic situation under consideration. From a methodological point of view, the constructed game model can be used as a new component of the content of applied mathematical training of a graduate of the University of Economics.
In practical applications, the tasks of strategic planning are complex and require many variant calculations when studying various scenarios, which are characterized by significant uncertainty in the forecast estimates. In this regard, the use of a complex of various means of information and analytical support for the activities of analysts and experts is relevant. Within the framework of this question, an information and analytical decision support system is proposed, focused on automating computational procedures in strategic planning. The system is organized on the basis of the Statistica computing platform and includes the platform's software tools, developed macros for describing and presenting statistical and analytical models, as well as decision support modules. The capabilities of the system are shown by specific examples of establishing patterns of development of Russian regions and cities in the real sector of the economy. The corresponding generalized models characterizing the state and development of regions by seven specific indicators in the period from 2012 to 2018 and by four specific indicators characterizing the development of cities in the period from 2003 to 2017 are obtained. It is established that the obtained models of collective behavior, presented in the form of equations of state, do not depend on time, but are determined only by the values of the achieved indicators. The proposed system allows you to increase the efficiency of the decisionmaking process, reduce the time and cost of developing strategic planning documents
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