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on Game Theory |
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Issue of 2011‒01‒16
thirteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Ana Paula Martins |
| Abstract: | This research states the stylised n (more than two) players’ splitting problem as a mathematical programme, relying on definitions of the values of the game and problem stationarity to generate tractable reduced forms, and derives the known solutions according to the properties of pertaining first-order conditions. On the one hand, boundary constraints are taken into consideration, required by the most general formulation possible with respect to the controls. On the other, distinction between FOC’s of optimizing behavior and equilibrium fitness is provided. Finally, the formal proof of the internal insufficiency of the usual approach to determine the equilibrium is advanced, and the imposing additional conditions – affecting cross multipliers - required for model solving forwarded and interpreted. Two different types of protocols (sets of rules of the game) were staged: alternate offers and synchronized ones. Perfect information (and foresight) of the players, infinite horizon, and offers exchange restricted to infinite-term settlements are always assumed. Each player makes a proposition of the division among the n participants. Periodic “outside” alternatives may differ according to whose offer is being analysed, and from those accruing to the players when none is forwarded. The alternate offers protocol is a generalization of the Rubinstein’s structure. At each round of negotiations, one and only one player, exogenously determined, can make an – the – offer. An agent must conciliate – and solve consistently – as many optimization problems as eventual proponents there are in the game. |
| Keywords: | Non-Cooperative N-Person Games, Infinite Horizon, Mixed Strategy Games, Mixed Strategies under Perfect Information Games, Simultaneous Sequential Bargaining, Matching Equilibrium under Sequential Bargaining, Synchronous (Decisions) Equilibrium under Sequential Bargaining, Mechanism Design, Bargaining Protocols, Dynamic Programming, Stationary Problems (without State Variables). |
| JEL: | C72 C78 C44 H56 D74 D31 C61 C62 |
| Date: | 2010–08–10 |
| URL: | http://d.repec.org/n?u=RePEc:eei:rpaper:eeri_rp_2010_36&r=gth |
| By: | David H. Wolpert; James Bono |
| Abstract: | Under its conventional positive interpretation, game theory predicts that the mixed strategy pro?le of players in a noncooperative game will satisfy some setvalued solution concept. Relative probabilities of pro?les in that set are unspeci?ed, and all pro?les not satisfying it are implicitly assigned probability zero. However the axioms underlying Bayesian rationality say that we should reason about player behavior using a probability density over all mixed strategy pro?les, not using a subset of all such pro?les. Such a density over pro?les can be viewed as a solution concept that is distribution-valued rather than set-valued. A distribution-valued concept provides a best single prediction for any noncooperative game, i.e., a universal re?nement. In addition, regulators can use a distribution-valued solution concept to make Bayes optimal choices of a mechanism, as required by Savage's axioms. In particular, they can do this in strategic situations where conventional mechanism design cannot provide advice. We illustrate all of this on a Cournot duopoly game. |
| Keywords: | Quantal Response Equilibrium, Bayesian Statistics, Entropic prior, Maximum entropy JEL Codes: C02, C11, C70, C72 |
| Date: | 2010–06 |
| URL: | http://d.repec.org/n?u=RePEc:amu:wpaper:2010-13&r=gth |
| By: | Ruud Hendrickx; Jacco Thijssen; Peter Borm |
| Abstract: | This paper discusses minimum cost spanning tree games and argues that the standard approach of using a transferable utility game to come up with a fair allocation of the total costs has some flaws. A new model of spillover games is presented, in which each agent's decision whether or not to cooperate is properly taken into account. |
| Keywords: | minimum cost spanning tree problems, transferable utility games, spillovers |
| JEL: | C71 C72 |
| Date: | 2011–01 |
| URL: | http://d.repec.org/n?u=RePEc:yor:yorken:11/02&r=gth |
| By: | David H. Wolpert; James Bono |
| Abstract: | In experiments it is typically found that many joint utility outcomes arise in any given unstructured bargaining game. This suggests using a positive unstructured bargaining concept that maps a bargaining game to a probability distribution over outcomes rather than to a single outcome. We show how to "translate" Nash's bargaining axioms to apply to such distributional bargaining concepts. We then prove that a subset of those axioms forces the distribution over outcomes to be a power-law. Unlike Nash's original result, our result holds even if the feasible set is finite. When the feasible set is convex and comprehensive, the mode of the power law distribution is the Harsanyi bargaining solution, and if we require symmetry it is the Nash bargaining solution. However in general these modes of the joint utility distribution are not Bayes-optimal predictions for the joint uitlity, nor are the bargains corresponding to those outcomes the most likely bargains. We then show how an external regulator can use distributional solution concepts to optimally design an unstructured bargaining scenario. Throughout we demonstrate our analysis in computational experiments involving flight rerouting negotiations in the National Airspace System. |
| Keywords: | JEL Codes: |
| Date: | 2010–11 |
| URL: | http://d.repec.org/n?u=RePEc:amu:wpaper:2010-14&r=gth |
| By: | Judith Avrahami (The Hebrew University of Jerusalem, Center for the Study of Rationality and School of Education); Werner Güth (Max Planck Institute of Economics, Strategic Interaction Group, Jena); Ralph Hertwig (University of Basel, Department of Psychology); Yaakov Kareev (The Hebrew University of Jerusalem, Center for the Study of Rationality and School of Education); Hironori Otsubo (Max Planck Institute of Economics, Strategic Interaction Group, Jena) |
| Abstract: | Whether behavior converges toward rational play or fair play in repeated ultimatum games depends on which player yields first. If responders concede first by accepting low offers, proposers would not need to learn to offer more, and play would converge toward unequal sharing. By the same token, if proposers learn fast that low offers are doomed to be rejected and adjust their offers accordingly, pressure would be lifted from responders to learn to accept such offers. Play would converge toward equal sharing. Here we tested the hypothesis that it is regret-both material and strategic-which determines how players modify their behavior. We conducted a repeated ultimatum game experiment with random strangers, in which one treatment does and another does not provide population feedback in addition to informing players about their own outcome. Our results show that regret is a good predictor of the dynamics of play. Specifically, we will turn to the dynamics that unfold when players make repeated decisions in the ultimatum game with randomly changing opponents, and when they learn not only about their own outcome in the previous round but also find out how the population on average has adapted to previous results (path dependence). |
| Keywords: | Ultimatum bargaining game, Reputation, Regret, Learning, Experiment |
| JEL: | C78 C92 |
| Date: | 2010–12–15 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2010-092&r=gth |
| By: | Amos Golan; James Bono |
| Abstract: | In this paper we formulate a solution concept without making assumptions about expected utility maximization, common knowledge or beliefs. Beliefs, strate- gies and the degree to which players are expected utility maximizers are endoge- nously determined as part of the solution. To achieve this, rather than solving the game from the players' point of view, we analyze the game as an "observer" who is not engaged in the process of the game. Our approach is an information theoretic one in which the observer utilizes an observation of play and the Maximum Entropy principle. We compare our solution concept with Bayesian Nash equilibrium and over the entropy ratio test as a method for determining the appropriateness of common modeling assumptions. We also demonstrate that the QRE concept can be signicantly generalized when viewed from the observer's perspective. For games of incomplete information we discover that alternative uses of the observer's information lead to alternative interpretations of rationality. These alternative in- terpretations of rationality may prove useful, especially in the context of ex post arbitration, as they indicate who is motivating whom. |
| Keywords: | incomplete information, entropy, information theory, pairwise rationality, QRE, endogenous rationality JEL Codes: C70, C79 |
| Date: | 2010–05 |
| URL: | http://d.repec.org/n?u=RePEc:amu:wpaper:2010-12&r=gth |
| By: | Karafyllis, Iasson; Jiang, Zhong-Ping; Athanasiou, George |
| Abstract: | This paper develops a novel methodology to study robust stability properties of Nash equilibrium points in dynamic games. Small-gain techniques in modern mathematical control theory are used for the first time to derive conditions guaranteeing uniqueness and global asymptotic stability of Nash equilibrium point for economic models described by functional difference equations. Specification to a Cournot oligopoly game is studied in detail to demonstrate the power of the proposed methodology. |
| Keywords: | Dynamic game; Cournot oligopoly; Nash equilibrium; Robust stability; Small gain |
| JEL: | C0 C02 C61 C70 C62 |
| Date: | 2010–01–07 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:26890&r=gth |
| By: | Karl Schlag (University of Vienna); Andriy Zapechelnyuk (Queen Mary, University of London) |
| Abstract: | Regret minimizing strategies for repeated games have been receiving increasing attention in the literature. These are simple adaptive behavior rules that exhibit nice convergence properties. If all players follow regret minimizing strategies, their average joint play converges to the set of correlated equilibria or to the Hannan set (depending on the notion of regret in use), or even to Nash equilibrium on certain classes of games. In this note we raise the question of validity of the regret minimization objective. By example we show that regret minimization can lead to unrealistic behavior, since it fails to take into account the effect of one's actions on subsequent behavior of the opponents. An amended notion of regret that corrects this defect is not very useful either, since achieving a no-regret objective is not guaranteed in that case. |
| Keywords: | Repeated games, Regret minimization, No-regret strategy |
| JEL: | C73 D81 |
| Date: | 2010–12 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp676&r=gth |
| By: | Lombardi, Michele |
| Abstract: | In a two-agent society with partially-honest agents, we extend Dutta and Sen (2009)'s results of Nash implementation to the domain of weak orders. We identify the class of Nash implementable social choice correspondences with a "gap" between necessary and sufficient conditions, both when exactly one agent is partially-honest and when both agents are partially-honest. We also show that, on the domain of linear orders, the "gap" between our conditions gets closed and they become equivalent to those devised by Dutta and Sen. New implementing mechanisms are devised. In line with earlier works, the classic condition of monotonicity is no longer required, whereas a weak version of the standard punishment condition is required even when both agents are known to be partially-honest. We derive simpler sufficient conditions that are satisfied in a wide range of applications. |
| Keywords: | Two-agent Nash implementation; intrinsic preferences for honesty; permissive results |
| JEL: | D71 C72 |
| Date: | 2010–12–22 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:27834&r=gth |
| By: | Villena, Mauricio G.; Zecchetto, Franco |
| Abstract: | The main aim of this article is to investigate the behavioral consequences of the provision of subject-specific information in the group effort levels chosen by players in an experimental CPR game. We examine two basic treatments, one with incomplete information and the other with complete information. In the former, subjects are informed only about their own individual payoffs and the aggregate extraction effort level of the group, and in the latter they are also informed about the individual effort levels and payoffs of each subject. Given this setting, the basic question we attempt to answer is: Will the provision of subject-specific performance information (i.e. individual’s effort levels and payoffs) improve or worsen the tragedy of the commons (i.e. an exploitation effort level greater than the socially optimum level)? In order to motivate our hypotheses and explain our experimental results at the individual level, we make use of the theory of learning in games, which goes beyond standard non-cooperative game theory, allowing us to explore the three basic benchmarks in the commons context: Nash equilibrium, Pareto efficient, and open access outcomes. We use several learning and imitation theoretical models that are based on contrasting assumptions about the level of rationality and the information available to subjects, namely: best response, imitate the average, mix of best response and imitate the average, imitate the best and follow the exemplary learning rules. Finally, in order to econometrically test the hypotheses formulated from the theoretical predictions we use a random-effects model to assess the explanatory power of the different selected behavioral learning and imitation rules. |
| Keywords: | Common Property Resources; Information; Learning and Imitation; Experimental Economics. |
| JEL: | D83 C72 C91 Q2 |
| Date: | 2010–01–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:27783&r=gth |
| By: | Francis Bloch (Ecole Polytechnique); David Cantala (El Colegio de México) |
| Abstract: | We analyze dynamic assignment problems where agents successively receive different objects (positions, offices, etc.). A finite set of n vertically differentiated indivisible objects are assigned to n agents who live n periods. At each period, a new agent enters society, and the oldest agent retires, leaving his object to be reassigned. We define independent assignment rules (where the assignment of an object to an agent is independent of the way other objects are allocated to other agents), efficient assignment rules (where there does not exist another assignment rule with larger expected surplus), and fair assignment rules (where agents experiencing the same circumstances have identical histories in the long run). When agents are homogenous, we characterize efficient, independent and fair rules as generalizations of the seniority rule. When agents draw their types at random, we prove that independence and efficiency are incompatible, and that efficient and fair rules only exist when there are two types of agents. We characterize two simple rules (type-rank and type-seniority) which satisfy both efficiency and fairness criteria in dichotomous settings. |
| Keywords: | dynamic assignment, finite Markov chains, seniority, promotion rules |
| JEL: | C78 D73 M51 |
| Date: | 2010–12 |
| URL: | http://d.repec.org/n?u=RePEc:emx:ceedoc:2010-18&r=gth |
| By: | Victor Aguirregabiria; Victor Aguirregabiria; Aviv Nevo; Aviv Nevo |
| Abstract: | Empirically studying dynamic competition in oligopoly markets requires dealing with large states spaces and tackling difficult computational problems, while handling heterogeneity and multiple equilibria. In this paper, we discuss some of the ways recent work in Industrial Organization has dealt with these challenges. We illustrate problems and proposed solutions using as examples recent work on dynamic demand for differentiated products and on dynamic games of oligopoly competition. Our discussion of dynamic demand focuses on models for storable and durable goods and surveys how researchers have used the \ |
| Keywords: | Industrial Organization; Oligopoly competition; Dynamic demand; Dynamic games; Estimation; Counterfactual experiments; Multiple equilibria; Inclusive values; Unobserved heterogeneity. |
| JEL: | L0 L1 |
| Date: | 2010–12–31 |
| URL: | http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-419&r=gth |
| By: | Matteo Triossi; Antonio Romero-Medina |
| Abstract: | 273 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:edj:ceauch:273&r=gth |