nep-gth New Economics Papers
on Game Theory
Issue of 2012‒08‒23
25 papers chosen by
Laszlo A. Koczy
Hungarian Academy of Sciences and Obuda University

  1. A Game with No Bayesian Approximate Equilibria By Ziv Hellman
  2. Transboundary Externalities and Property Rights: An International River Pollution Model By Gerard van der Laan; Nigel Moes
  3. Level-k Reasoning and Incentives By Larbi Alaoui; Antonio Penta
  4. On the (im)possibility of improving upon the student-proposing deferred acceptance mechanism By Kesten, Onur; Kurino, Morimitsu
  5. A Bankruptcy Approach to the Core Cover By Arantza Estévez-Fernández; María Gloria Fiestras-Janeiro; Manuel Alfredo Mosquera; Estela Sánchez- Rodríguez
  6. Codes of Conduct, Private Information and Repeated Games By Juan I Block; David K Levine
  7. Solidarity and fair taxation in TU games By Casajus, André
  8. Competition for a Majority By Barelli, Paulo; Govindan, Srihari; Wilson, Robert
  9. A Concessions-Based Mechanism for Meta-Bargaining Problems By Marco-Gil, Maria del Carmen; Peris, Josep E.; Subiza, Begoña
  10. The Intrinsic Comparative Dynamics of Locally Differentiable Feedback Nash Equilibria of Autonomous and Exponentially Discounted Infinite Horizon Differential Games By Micahel Caputo; Chen Ling
  11. On the location of public bads: strategy-proofness under two-dimensional single-dipped preferences By Öztürk Murat; Peters Hans; Storcken Ton
  12. Strategy-proofness and Efficiency with Nonquasi-linear Preferences: A Characterization of Minimum Price Walrasian Rule By Shuhei Morimoto; Shigehiro Serizawa
  13. Share Functions for Cooperative Games with Levels Structure of Cooperation By Mikel Alvarez-Mozos; Rene van den Brink; Gerard van der Laan; Oriol Tejada
  14. Designing for Diversity: Matching with Slot-Specific Priorities By Scott Duke Kominers; Tayfun Sönmez
  15. The Importance of Irrelevance of Rejected Contracts in Matching under Weakened Substitutes Conditions By Orhan Aygün; Tayfun Sönmez
  16. Matching with Contracts: The Critical Role of Irrelevance of Rejected Contracts By Orhan Aygün; Tayfun Sönmez
  17. Backward induction or forward reasoning? An experiment of stochastic alternating offer bargaining By Berninghaus, Siegfried K.; Güth, Werner; Schosser, Stephan
  18. Confirming Information Flows in Networks By Pascal Billand; Christophe Bravard; Jurjen Kamphorst; Sudipta Sarangi
  19. On the Existence and Stability of Pareto Optimal Endogenous Matching with Fairness By Dai, Darong
  20. The Importance of Knowing Your Own Reputation By Matthias Greiff; Fabian Paetzel
  21. Extending the Nash solution to choice problems with reference points By Sudhölter, Peter; Zarzuelo, José M.
  22. Motives of Sanctioning: Equity and Emotions in a Public Good Experiment with Punishment By Paolo Crosetto; Werner Güth; Luigi Mittone; Matteo Ploner
  23. Cooperation in a Risky Environment: Decisions from Experience in a Stochastic Social Dilemma By Florian Artinger; Nadine Fleischhut; M. Vittoria Levati; Jeffrey R. Stevens
  24. Nullifying vs. dummifying players or nullified vs. dummified players: The difference between the equal division value and the equal surplus division value By Casajus, André; Hüttner, Frank
  25. A New Stationary Game Equilibrium Induced by Stochastic Group Evolution and Rational Individual Choice By Dai, Darong; Shen, Kunrong

  1. By: Ziv Hellman
    Abstract: Simon (2003) presented an example of a 3-player Bayesian games with no Bayesian equilibria but it has been an open question whether or not there are games with no approximate Bayesian equilibria. We present an example of a Bayesian game with two players, two actions and a continuum of states that possesses no approximate Bayesian equilibria, thus resolving the question. As a side benefit we also have for the first time an an example of a 2-player Bayesian game with no Bayesian equilibria and an example of a strategic-form game with no approximate Nash equilibria. The construction makes use of techniques developed in an example by Y. Levy of a discounted stochastic game with no stationary equilibria.
    Date: 2012–07
  2. By: Gerard van der Laan (VU University Amsterdam); Nigel Moes (VU University Amsterdam)
    Abstract: In this paper we study international river pollution problems. We introduce a model in which the agents (countries) located along a river derive benefit while causing pollution, but also incur environmental costs of experiencing pollution from all upstream agents. We find that total pollution in the model decreases when the agents decide to cooperate. The resulting gain in social welfare can be distributed among the agents based on the property rights over the river. Using principles from international water law we suggest 'fair' ways of distributing the property rights and therefore the cooperative gain.
    Keywords: international river; pollution; externality; property rights; value
    JEL: C70 D60 Q53
    Date: 2012–01–19
  3. By: Larbi Alaoui; Antonio Penta
    Abstract: Level-k theories are agnostic over whether individuals stop the iterated reasoning because of their own cognitive constraints, or because of their beliefs over the cognitive constraints of their opponents. In practice, individual level of play may be a function both of their own constraints and their beliefs over their opponents' reasoning process. Moreover, the rounds of introspection that players perform may depend on their incentives to think more deeply. We develop a theory which explicitly models players' reasoning procedure. The rounds of introspection that individuals perform and their actual level of play both follow endogenously. This model delivers testable implications as payoff s and opponents change, and it allows for comparisons across games. It also disentangles the cognitive bound of players for a given game from their beliefs about the play of their opponents. In conjunction with the framework, we present an experiment designed to test its predictions. We modify the Arad and Rubinstein (2012) '11-20' game to serve this precise purpose, and administer different treatments which vary beliefs over payoff s and opponents. The results of this experiment are consistent with the model, and appear to lend support to our theory. This experiment also confirms the central premise that individuals change their level of play as incentives to think more and beliefs over opponents vary.
    Keywords: beliefs, bounded rationality, cognitive cost, higher order beliefs, incentives, level-k reasoning, value of reasoning
    JEL: C72 C92 D80 D83
    Date: 2012–07
  4. By: Kesten, Onur; Kurino, Morimitsu
    Abstract: This paper studies a general school choice problem with or without outside options. The Gale-Shapley student-proposing deferred acceptance mechanism (DA) has played a central role not only in theory but also in important practical applications. We show that in problems where some students cannot credibly submit a single school as the only acceptable option, it is possible to improve upon DA without sacrificing strategyproofness. On the other hand, in unrestricted problems where no outside options necessarily exist, it is not possible to improve upon DA via a strategy-proof mechanism. -- Es wird ein allgemeines school-choice-Problem untersucht mit und ohne outside options. Der Gale-Shapley student-proposing deferred acceptance-Mechanismus (DA) spielt eine zentrale Rolle nicht nur in der Theorie sondern auch in wichtigen praktischen Anwendungen. Wir zeigen, dass in Situationen, in denen einige Schüler nicht glaubwürdig nur eine einzige Schule als akzeptable Option angeben können, der DA verbessert werden kann, ohne dass die Nichtmanipulierbarkeit (strategy proofness) des Mechanismus dafür geopfert werden muss. Auf der anderen Seite gilt für Situationen, in denen nicht notwendigerweise outside options existieren, dass der DA nicht verbessert werden kann mit Hilfe eines nichtmanipulierbaren Mechanismus.
    Keywords: student-proposing deferred acceptance mechanism,strategy-proofness,Pareto dominance,outside options
    JEL: C78 D78 I21
    Date: 2012
  5. By: Arantza Estévez-Fernández (VU University Amsterdam); María Gloria Fiestras-Janeiro (Vigo University); Manuel Alfredo Mosquera (Vigo University); Estela Sánchez- Rodríguez (Vigo University)
    Abstract: In this paper we establish a relationship between the core cover of a compromise admissible game and the core of a particular bankruptcy game: the core cover of a compromise admissible game is, indeed, a translation of the set of coalitional stable allocations captured by an associated bankruptcy game. Moreover, we analyze the combinatorial complexity of the core cover and, consequently, of the core of a compromise stable game.
    Keywords: Cooperative game theory; compromise admissible games; bankruptcy; core cover; complexity
    JEL: C71
    Date: 2012–02–10
  6. By: Juan I Block; David K Levine
    Date: 2012
  7. By: Casajus, André
    Abstract: We consider an analytic formulation/parametrization of the class of efficient, linear, and symmetric values for TU games that, in contrast to previous approaches, which rely on the standard basis, rests on the linear representation of TU games by unanimity games. Unlike most of the other formulae for this class, our formula allows for an economic interpretation in terms of taxing the Shapley payoffs of unanimity games. We identify those parameters for which the values behave economically sound, i.e., for which the values satisfy desirability and positivity. Put differently, we indicate requirements on fair taxation in TU games by which solidarity among players is expressed. --
    Keywords: shapley value,solidarity,taxation,desirability,positivity
    JEL: C71 D60
    Date: 2012
  8. By: Barelli, Paulo (University of Rochester); Govindan, Srihari (University of Rochester); Wilson, Robert (Stanford University)
    Abstract: We define the class of two-player zero-sum games with payoffs having mild discontinuities, which in applications typically stem from how ties are resolved. For games in this class we establish sufficient conditions for existence of a value of the game and minimax or Nash equilibrium strategies for the players. We prove first that if all discontinuities favor one player then a value exists and that player has a minimax strategy. Then we establish that a general property called payoff approachability implies that the value results from equilibrium. We prove further that this property implies that every modification of the discontinuities yields the same value; in particular, for every modification, epsilon-equilibria exist. We apply these results to models of elections in which two candidates propose policies and a candidate wins election if a weighted majority of voters prefer his policy. We provide tie-breaking rules and assumptions on voters' preferences sufficient to imply payoff approachability, hence existence of equilibria, and each other tie-breaking rule yields the same value and has epsilon-equilibria. These conclusions are also derived for the special case of Colonel Blotto games in which each candidate allocates his available resources among several constituencies and the assumption on voters' preferences is that a candidate gets votes from those constituencies allocated more resources than his opponent offers. Moreover, for the case of simple-majority rule we prove existence of an equilibrium that has zero probability of ties.
    JEL: C62 C72 D72
    Date: 2012–06
  9. By: Marco-Gil, Maria del Carmen (Universidad Politécnica de Cartagena, Department of Economics); Peris, Josep E. (Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica); Subiza, Begoña (Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica)
    Abstract: In 1950, Nash's seminal paper introduced the axiomatic approach to the analysis of bargaining situations. Since then, many bargaining solutions have appeared and been axiomatically analyzed. The fact that agents, when face a bargaining problem, can come up with different solution concepts (that is, di§erent notions of fairness and equity) was first introduced by van Damme (1986) by means of the meta-bargaining model. In this paper we present and axiomatically analyze a mechanism for solving meta-bargaining problems, which we call Unanimous-Concession. As an example, we show that the Nash solution is the result of the meta-bargaining process we define, when agents have dual egalitarian criteria. Finally, we compare, from an axiomatic and descriptive point of view, our proposal with other meta-bargaining mechanisms.
    Keywords: bargaining problem; mechanism; meta-bargaining; axiomatic approach
    JEL: C71 D63 D71
    Date: 2012–07–24
  10. By: Micahel Caputo (University of Central Florida, Orlando, FL); Chen Ling (Southwestern University of Finance and Economics, Chengdu, Sichuan, China)
    Abstract: The comparative dynamics of locally differentiable feedback Nash equilibria are derived for the ubiquitous class of autonomous and exponentially discounted infinite horizon differential games. The resulting refutable implications are intrinsic to the said class of differential games, and thus form their basic, empirically testable, properties. Their relationship with extant results in optimal control theory and static game theory is discussed. Separability conditions are identified on the instantaneous payoff and transition functions under which the intrinsic comparative dynamics collapse, in form, to those in optimal control problems. Applications of the results to capital accumulation and sticky-price games are provided.
    Keywords: comparative dynamics, differential games, feedback Nash equilibria
    JEL: C72 C73 L13
    Date: 2012–07
  11. By: Öztürk Murat; Peters Hans; Storcken Ton (METEOR)
    Abstract: In a model with finitely many agents who have single-dipped Euclidean preferences on a polytope inthe Euclidean plane, a rule assigns to each profile of reported dips a point of the polytope. Asingle-best point is a point which is the unique point at maximal distance from some other pointof the polytope. It is proved that any strategy-proof and Pareto optimal rule is a dictatorshipunless the polytope has exactly two single-best points or it has exactly four single-best pointswhich form the vertices of a rectangle. In the latter cases strategy-proof and Pareto optimalrules can be obtained by committee voting (simple games) between the single-best alternatives.This framework models situations where public bads such as garbage dumping grounds or nuclearplants have to be located within a confined region.
    Keywords: public economics ;
    Date: 2012
  12. By: Shuhei Morimoto; Shigehiro Serizawa
    Abstract: We consider the problems of allocating several heterogeneous objects owned by governments to a group of agents and how much agents should pay. Each agent receives at most one object and has nonquasi-linear preferences. Nonquasi-linear preferences describe environments in which large-scale payments influence agents' abilities to utilize objects or derive benefits from them. The "minimum price Walrasian (MPW) rule" is the rule that assigns a minimum price Walrasian equilibrium allocation to each preference profile. We establish that the MPW rule is the unique rule that satisfies the desirable properties of strategy-proofness, Pareto-efficiency, individual rationality, and nonnegative payment on the domain that includes nonquasi-linear preferences. This result does not only recommend the MPW rule based on those desirable properties, but also suggest that governments cannot improve upon the MPW rule once they consider them essential. Since the outcome of the MPW rule coincides with that of the simultaneous ascending (SA) auction, our result explains the pervasive use of the SA auction.
    Date: 2012–08
  13. By: Mikel Alvarez-Mozos (University of Santiago de Compostela); Rene van den Brink (VU University Amsterdam); Gerard van der Laan (VU University Amsterdam); Oriol Tejada (ETH Zuerich)
    Abstract: In a standard TU-game it is assumed that every subset of the player set can form a coalition and earn its worth. One of the first models where restrictions in cooperation are considered is the one of games with coalition structure. In such games the player set is partitioned into unions and players can only cooperate within their own union. Owen introduced a value for games with coalition structure under the assumption that also the unions can cooperate among them. Winter extended this value to games with levels structure of cooperation, which consists of a game and a finite sequence of partitions defined on the player set, each of them being coarser than the previous one. A share function for TU-games is a type of solution that assigns to every game a vector whose components add up to one, and thus they can be interpreted as players' shares in the worth to be allocated. Extending the approach to games with coalition structure developed by van den Brink and van der Laan (2005), we introduce a class of share functions for games with levels structure of cooperation by defining, for each player and each level, a standard TU-game. The share given to each player is then defined as the product of her shares in the games at every level. We show several desirable properties and provide axiomatic characterizations of this class of LS-share functions.
    Keywords: cooperative game; Shapley value; coalition structure; share functions; levels structure of cooperation
    JEL: C71
    Date: 2012–05–11
  14. By: Scott Duke Kominers (Becker Friedman Institute, University of Chicago); Tayfun Sönmez (Boston College)
    Abstract: To encourage diversity, branches may vary contracts' priorities across slots. The agents who match to branches, however, have preferences only over match partners and contractual terms. Ad hoc approaches to resolving agents' indifferences across slots in the Chicago and Boston school choice programs have introduced biases, which can be corrected with more careful market design. Slot-specific priorities can fail the substitutability condition typically crucial for outcome stability. Nevertheless, an embedding into a one-to-one agent--slot matching market shows that stable outcomes exist and can be found by a cumulative offer mechanism that is strategy-proof and respects unambiguous improvements in priority.
    Keywords: Market Design, Matching with Contracts, Stability, Strategy-Proofness, School Choice, Affirmative Action
    JEL: C78 D63 D78
    Date: 2012–07–02
  15. By: Orhan Aygün (Boston College); Tayfun Sönmez (Boston College)
    Abstract: We show that Hatfield and Kojima (2010) inherits a critical ambiguity from its predecessor Hatfield and Milgrom (2005), and clearing this ambiguity has strong implications for the paper. Of the two potential remedies, the first one results in the failure of all theorems except one in the absence of an additional irrelevance of rejected contracts (IRC) condition, whereas the second remedy eliminates the transparency of the results, reduces the scope of the model, and contradicts authors' interpretation of the nature of their contributions. Fortunately all results are restored when IRC is explicitly assumed under the first remedy.
    Keywords: Matching with Contracts, Stability, Market Design
    JEL: C78 D63 D78
    Date: 2012–06–30
  16. By: Orhan Aygün (Boston College); Tayfun Sönmez (Boston College)
    Abstract: We show that an ambiguity in setting the primitives of the matching with contracts model by Hatfield and Milgrom (2005) has serious implications for the model. Of the two ways to clear the ambiguity, the first (and what we consider more "clean") remedy renders several of the results of the paper invalid in the absence of an additional irrelevance of removed contracts condition implicitly assumed throughout the paper, whereas the second remedy results in the lack of transparency in presentation of results while at the same time reducing the scope of the analysis with no clear benefit.
    Keywords: Matching with Contracts, Stability, Market Design
    JEL: C78 D63 D78
    Date: 2012–05–31
  17. By: Berninghaus, Siegfried K.; Güth, Werner; Schosser, Stephan
    Abstract: Bounded rationality questions backward induction, which however, does not exclude such reasoning when anticipation is easy. In our stochastic (alternating offer) bargaining experiment, there is a certain first-period pie and a known finite deadline. What is uncertain (except for the final period) is whether there is a further period. Whereas backward induction requires information about all later pie sizes and probabilities, forward reasoning is expected to consider only the immediate prospects. Rather than relying only on decision data, we try to assess the cognitive approach such as forward reasoning of backward induction by control of information retrieval. We find that participants who begin with the shortest games before playing possibly longer games, initially resort to backward induction before switching to forward-looking behavior. --
    Keywords: backward induction,forward reasoning,bargaining
    JEL: C70 C72 C91
    Date: 2012
  18. By: Pascal Billand (Universite de Lyon, Universite Jean Monnet, Saint-Etienne, CNRS, GATE); Christophe Bravard (Universite de Lyon, Universite Jean Monnet, Saint-Etienne, CNRS, GATE); Jurjen Kamphorst (Erasmus University Rotterdam); Sudipta Sarangi (DIW Berlin and Louisiana State University)
    Abstract: Social networks, be it on the internet or in real life, facilitate information flows. We model this by giving agents incentives to link with others and receive information through those links. In many networks agents will value confirmation of the information they receive from others. Our paper analyzes the impact such a need for confirmation has on the social networks which are formed. We first study the existence of Nash equilibria and then characterize the set of strict Nash networks. Next, we characterize the set of strictly efficient networks and discuss the relationship between strictly efficient networks and strict Nash networks.
    Keywords: connections model; confirmation; two-way flow models
    JEL: C72 D85
    Date: 2012–03–01
  19. By: Dai, Darong
    Abstract: In the current paper, we study the asymmetric normal-form game between two heterogeneous groups of populations by employing the stochastic replicator dynamics driven by Lévy process. A new game equilibrium, i.e., the game equilibrium of a stochastic differential cooperative game on time, is derived by introducing optimal-stopping technique into evolutionary game theory, which combines with the Pareto optimal standard leads us to the existence of Pareto optimal endogenous matching. Moreover, stability of the Pareto optimal endogenous matching is confirmed by essentially using the well-known Girsanov Theorem.
    Keywords: Stochastic differential cooperative game on time; Endogenous matching; Stability; Fairness; Adaptive learning
    JEL: C78 C70 C62
    Date: 2012–08–08
  20. By: Matthias Greiff (University of Giessen); Fabian Paetzel (University of Bremen)
    Abstract: We experimentally investigate a ?nitely repeated public good game with varying partners. Within each period, participants are pairwise matched and contribute simultaneously. Participants are informed about contributions and each participant evaluates her partner’s contribution. At the beginning of the next period, participants are re-matched and, except for the two control treatments, receive information resulting from the previous period’s evaluations. There are three information treatments: Participants receive information either about their own evaluation or about their partner’s evaluation or both. Although participants condition their contributions on their partners’ evaluations, this information alone is insuf?cient to raise contributions. Only if participants also know their own evaluation, we do ?nd a signi?cant increase in contributions relative to the control treatments.
    Keywords: Conditional Cooperation, Evaluation, Public Good Games, Prisoner’s Dilemma, Repeated games with varying partners, Reputation, Second-order beliefs.
    JEL: C72 C91 D03 D83
    Date: 2012
  21. By: Sudhölter, Peter (Department of Business and Economics); Zarzuelo, José M. (Faculty of Economics and Business Administration)
    Abstract: In 1985 Aumann axiomatized the Shapley NTU value by non-emptiness, efficiency, unanimity, scale covariance, conditional additivity, and independence of irrelevant alternatives. We show that, when replacing unanimity by "unanimity for the grand coalition" and translation covariance, these axioms characterize the Nash solution on the class of n-person choice problems with reference points. A classical bargaining problem consists of a convex feasible set that contains the disagreement point here called reference point. The feasible set of a choice problem does not necessarily contain the reference point and may not be convex. However, we assume that it satisfies some standard properties. Our result is robust so that the characterization is still valid for many subclasses of choice problems, among those is the class of classical bargaining problems. Moreover, we show that each of the employed axioms – including independence of irrelevant alternatives – may be logically independent of the remaining axioms.
    Keywords: Bargaining problem; Nash set; Shapley NTU value
    JEL: C71 C78
    Date: 2012–08–13
  22. By: Paolo Crosetto (Max Planck Institute of Economics, Strategic Interaction Group, Jena, Germany); Werner Güth (Max Planck Institute of Economics, Strategic Interaction Group, Jena, Germany); Luigi Mittone (Department of Economics - CEEL, University of Trento, Italy); Matteo Ploner (Department of Economics - CEEL, University of Trento, Italy)
    Abstract: We study conditional cooperation based on a sequential two-person linear public good game in which a trusting first contributor can be exploited by a second contributor. After playing this game the first contributor is allowed to punish the second contributor. The consequences of sanctioning depend on the treatment: whereas punishment can reduce inequality in one treatment, it only creates another inequality in the other. To capture the effect of delay on punishment both treatments are run once with immediate and once with delayed punishment. Moreover, to investigate the effect of pure voice, all four treatments are also run in a virtual condition with no monetary consequences of punishment. Results show the emergence across all conditions of a strong norm of conditional cooperation. Punishment is generally low, it is higher when not delayed and it is not used to reduce inequality in payoffs. The main motive of sanctioning appears to be the need to punish a violation of the reciprocity norm, irrespective of monetary consequences.
    Keywords: Public good games, Punishment, Experiments, Conditional cooperation
    JEL: C70 C72 C92 H41
    Date: 2012–08–20
  23. By: Florian Artinger (Max Planck Institute for Human Development, Berlin); Nadine Fleischhut (Max Planck Institute for Human Development, Berlin); M. Vittoria Levati (Max Planck Institute of Economics, Jena, and Department of Economics, University of Verona); Jeffrey R. Stevens (Department of Psychology, Nebraska)
    Abstract: Often in cooperative situations, many aspects of the decision-making environment are uncertain. We investigate how cooperation is shaped by the way information about risk is presented (from description or from experience) and by differences in risky environments. Drawing on research from risky choice, we compare choices in stochastic social dilemmas to those in lotteries with equivalent levels of risk. Cooperation rates in games vary with different levels of risk across decision situations with the same expected outcomes, thereby mimicking behavior in lotteries. Risk presentation, however, only affected choices in lotteries, not in stochastic games. Process data suggests that people respond less to probabilities in the stochastic social dilemmas than in the lotteries. The findings highlight how an uncertain environment shapes cooperation and call for models of the underlying decision processes.
    Keywords: Decisions from Experience, Social Dilemma, Cooperation, Risky Choice, Public Good.
    JEL: C72 C73 C92 D81
    Date: 2012–08–20
  24. By: Casajus, André; Hüttner, Frank
    Abstract: We provide new characterizations of the equal surplus division value and the equal division value as well as of the class of their convex mixtures. This way, the difference between the Shapley value, the equal division value, and the equal surplus division value is pinpointed to one axiom. Moreover, we shed light on solidarity principles embodied in the equal division value and in the equal surplus division values. --
    Keywords: solidarity,nullifying player,equal division value,equal surplus division value,desirability
    JEL: C71 D60
    Date: 2012
  25. By: Dai, Darong; Shen, Kunrong
    Abstract: In the present paper, a new approach to equilibrium selection for very general normal form games has been constructed by introducing stochastic optimal stopping theory into classical evolutionary game theory. That is, the new game equilibrium is induced by both stochastic group evolution and decentralized rational individual choice. Moreover, stability of the game equilibrium is confirmed from both time and space dimensions.
    Keywords: Stochastic replicator dynamics; Rational choice; Normal-form game; Stability
    JEL: C70 C62
    Date: 2012–01–15

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