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on Game Theory |
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Issue of 2012‒02‒27
fifteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Johannes Horner (Cowles Foundation, Yale University); Satoru Takahashi (Dept. of Economics, Princeton University); Nicolas Vieille (HEC Paris) |
| Abstract: | This paper provides a dual characterization of the limit set of perfect public equilibrium payoffs in stochastic games (in particular, repeated games) as the discount factor tends to one. As a first corollary, the folk theorems of Fudenberg, Levine and Maskin (1994), Kandori and Matsushima (1998) and Hörner, Sugaya, Takahashi and Vieille (2011) obtain. As a second corollary, in the context of repeated games, it follows that this limit set of payoffs is a polytope (a bounded polyhedron) when attention is restricted to equilibria in pure strategies. We provide a two-player game in which this limit set is not a polytope when mixed strategies are considered. |
| Keywords: | Stochastic games, Repeated games, Folk theorem |
| JEL: | C72 C73 |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1848&r=gth |
| By: | Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics); Peter Sudhölter (University of Southern Denmark) |
| Abstract: | An element of the possibly unbounded core of a cooperative game with precedence constraints belongs to its bounded core if any transfer to a player from any of her subordinates results in payoffs outside the core. The bounded core is the union of all bounded faces of the core, it is nonempty if the core is nonempty, and it is a continuous correspondence on games with coinciding precedence constraints. If the precedence constraints generate a connected hierarchy, then the core is always nonempty. It is shown that the bounded core is axiomatized similarly to the core for classical cooperative games, namely by boundedness (BOUND), nonemptiness for zero-inessential two-person games (ZIG), anonymity, covariance under strategic equivalence (COV), and certain variants of the reduced game property (RGP), the converse reduced game property (CRGP), and the reconfirmation property. The core is the maximum solution that satisfies a suitably weakened version of BOUND together with the remaining axioms. For games with connected hierarchies, the bounded core is axiomatized by BOUND, ZIG, COV, and some variants of RGP and CRGP, whereas the core is the maximum solution that satisfies the weakened version of BOUND, COV, and the variants of RGP and CRGP. |
| Keywords: | TU game, core, restricted cooperation. |
| JEL: | C71 |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:12006&r=gth |
| By: | Tao Wang (Queen's University) |
| Abstract: | In this paper, we analyze the asymmetric pure strategy equilibria in a dynamic game of pure information externality. Each player receives a private signal and chooses whether and when to invest. In some of the periods, only a subgroup of the players make decisions, which we call bunching, while the rest of the players do not invest regardless of their signals. Bunching is different from herding; it occurs in the first period and recursively until herding takes place or the game runs out of undecided players. We find that any asymmetric pure strategy equilibrium is more efficient than the symmetric mixed strategy equilibrium. When players become patient enough, herding of investment disappears in the most efficient asymmetric pure strategy equilibrium, while the least efficient asymmetric pure strategy equilibrium resembles those in a fixed timing model, producing an exact match when the discount factor is equal to 1. Bunch sizes are shown to be independent of the total number of players; adding more players to the game need not change early players' behavior. All these are unique properties of the asymmetric pure strategy equilibria. We also show that the asymmetric pure strategy equilibria can accommodate small heterogeneities of the players in costs of acquiring signals, discount factors, or degree of risk aversion. In any of these environments, there exists a unique welfare maximizing equilibrium which provides a natural way for the players to coordinate. |
| Keywords: | bunching, herding, endogenous timing, asymmetric equilibrium, information externality |
| JEL: | C73 D82 G01 |
| Date: | 2011–11 |
| URL: | http://d.repec.org/n?u=RePEc:qed:wpaper:1291&r=gth |
| By: | Alex Gershkov; Jacob Goeree; Alexey Kushnir; Benny Moldovanu; Xianwen Shi |
| Abstract: | We consider a standard social choice environment with linear utilities and independent, one-dimensional, private types. We prove that for any Bayesian incentive compatible mechanism there exists an equivalent dominant strategy incentive compatible mechanism that delivers the same interim expected utilities for all agents and the same ex ante expected social surplus. The short proof is based on an extension of an elegant result due to Gutmann et al. (Annals of Probability, 1991). We also show that the equivalence between Bayesian and dominant strategy implementation generally breaks down when the main assumptions underlying the social choice model are relaxed, or when the equivalence concept is strengthened to apply to interim expected allocations. |
| Keywords: | Bayesian Implementation, Dominant Strategy Implementation, Equivalence |
| JEL: | D82 |
| Date: | 2012–02–16 |
| URL: | http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-445&r=gth |
| By: | Andrweas Leibbrandt (Department of Economics, Monash University, Australia); Abhijit Ramalingam (School of Economics and Centre for Behavioural and Experimental Social Science, and University of East Anglia, Norwich, United Kingdom); Lauri Sääksvuori (Strategic Interaction Group, Max Planck Institute of Economics, Jena, Germany); James M. Walker (Department of Economics and Workshop in Political Theory and Policy Analysis, Indiana University, United States) |
| Abstract: | Abundant evidence suggests that high levels of contributions to public goods can be sustained through self-governed monitoring and sanctions. This experimental study investigates the effectiveness of decentralized sanctioning institutions where punishment opportunities are restricted to agents who are linked through alternative punishment networks. We find that the structure of the punishment network significantly impacts contributions to the public good, but not overall efficiencies. Contributions collapse over decision rounds in groups with limited punishment opportunities, even if the absolute punishment capacity corresponds to the complete punishment network where all agents are allowed to punish each other. However, after allowing for the costs of sanctions, efficiencies are similar across the different networks that allow for punishment and the no-punishment network. |
| Keywords: | public goods experiment, punishment, cooperation, networks |
| JEL: | C92 D01 D03 H41 |
| Date: | 2012–02–02 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2012-004&r=gth |
| By: | Saglam, Ismail |
| Abstract: | In this paper, we present a simple axiomatization of the n-person egalitarian solution. The single axiom sufficient for characterization is a new condition which we call symmetric decomposition. |
| Keywords: | Cooperative bargaining; egalitarian solution |
| JEL: | C78 C71 |
| Date: | 2012–02–19 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:36773&r=gth |
| By: | Werner Güth (Max Planck Institute of Economics, Strategic Interaction Group); M. Vittoria Levati (Max Planck Institute of Economics, Jena, Germany, and Department of Economics, University of Verona, Verona, Italy); Natalia Montinari (Max Planck Institute of Economics, Jena, Germany) |
| Abstract: | We introduce a procedurally fair rule to study a situation where people disagree about the value of three alternatives in the way captured by the voting paradox. The rule allows people to select a final collective ranking by submitting a bid vector with six components (the six possible rankings of the three alternatives). In a laboratory experiment we test the robustness of the rule to the introduction of subsidies and taxes. We have two main results. First, in all treatments, the most frequently chosen ranking is the socially efficient one. Second, subsidies slightly enhance overbidding. Furthermore, an analysis of individual bid vectors reveals interesting behavioral regularities. |
| Keywords: | Bidding behavior, Procedural fairness, Voting paradox |
| JEL: | C92 D02 D71 |
| Date: | 2012–02–20 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2012-005&r=gth |
| By: | Gächter, Simon (University of Nottingham); Nosenzo, Daniele (University of Nottingham); Sefton, Martin (University of Nottingham) |
| Abstract: | We compare social preference and social norm based explanations for peer effects in a three-person gift-exchange game experiment. In the experiment a principal pays a wage to each of two agents, who then make effort choices sequentially. In our baseline treatment we observe that the second agent's effort is influenced by the effort choice of the first agent, even though there are no material spillovers between agents. This peer effect is predicted by a model of distributional social preferences (Fehr-Schmidt, 1999). As we show from a norms-elicitation experiment, it is also consistent with social norms compliance. A conditional logit investigation of the explanatory power of payoff inequality and elicited norms finds that the second agent's effort can be best explained by the social preferences model. In further treatments with modified games we find that the presence/strength of peer effects changes as predicted by the social preferences model. As with the baseline treatment, a conditional logit analysis favors an explanation based on social preferences, rather than social norms following for these treatments. Our results suggest that, in our context, the social preferences model provides a parsimonious explanation for the observed peer effect. |
| Keywords: | peer effects, social influence, gift-exchange, experiment, social preferences, inequity aversion, measuring social norms |
| JEL: | A13 C92 D03 |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp6345&r=gth |
| By: | Lombardi, Michele; Yoshihara, Naoki |
| Abstract: | The paper proposes necessary and suffi cient conditions for the natural implementation of (efficient) social choice correspondences (SCCs) in pure finite exchange economies when some of the agents are partially honest. A partially honest agent is an agent who strictly prefers to tell the truth when lying has no better material consequences for her. Firstly, it is shown that if there is even one partially honest agent in the economy (and the planner does not know her identity), then any SCC is Nash implementable by a natural price-allocation mechanism. Secondly, and in sharp contrast with the results of conventional models of natural implementation, it is shown that the equivalence relationship between natural price-allocation mechanisms and natural price-quantity2 mechanisms no longer holds. Finally, and even more strikingly, the paper reports that the class of implementable SCCs by natural price-quantity mechanisms is significantly enlarged. |
| Keywords: | Natural implementation, Nash equilibrium, exchange economies, intrinsic preferences for honesty |
| JEL: | C72 D71 |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:hit:hituec:561&r=gth |
| By: | Christoph Bühren (University of Kassel); Björn Frank (University of Kassel); Rosemarie Nagel (University Pompeu Fabra) |
| Abstract: | Alain Ledoux, who was one of over 6,000 chess players taking part in Bühren and Frank´s (2012) online Beauty Contest experiment, turned out to be the forgotten inventor of that game. We reconstruct the birth of the Beauty Contest. In section 1 of our note, its first two authors outline the history of the game that metamorphosed into the famous guessing game experiment which was first run in the lab by Rosemarie Nagel. In section 2, Rosemarie Nagel adds further remarks and thoughts about the development of the experimental Beauty Contest. |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:mar:magkse:201211&r=gth |
| By: | Corchon, Luis C.; Triossi, Matteo |
| Abstract: | In this paper, we present a model of implementation where infeasible allocations are converted into feasible ones through a process of renegotiation that is represented by a reversion function. We describe the maximal set of Social Choice Correspondences that can be implemented in Nash Equilibrium in a class of reversion functions that punish agents for infeasibilities. This is used to study the implementation of the Walrasian Correspondence and several axiomatic solutions to problems of bargaining and taxation. |
| Keywords: | Teoría de juegos; Toma de decisiones; Economía del bienestar; |
| Date: | 2011–02 |
| URL: | http://d.repec.org/n?u=RePEc:ner:carlos:info:hdl:10016/13427&r=gth |
| By: | Erik O. Kimbrough (Department of Economics (AE1), School of Business and Economics, Maastricht University); Roman M. Sheremeta (Argyros School of Business and Economics, Chapman University) |
| Abstract: | Conflict and competition often impose costs on both winners and losers, and conflicting parties may prefer to resolve the dispute before it occurs. The equilibrium of a conflict game with side-payments predicts that with binding offers, proposers make and responders accept side-payments, generating settlements that strongly favor proposers. When side-payments are non-binding, proposers offer nothing and conflicts always arise. Laboratory experiments confirm that binding side-payments reduce conflicts. However, 30% of responders reject binding offers, and offers are more egalitarian than predicted. Surprisingly, non-binding side-payments also improve efficiency, although less than binding. With binding side-payments, 87% of efficiency gains come from avoided conflicts. However, with non-binding side-payments, only 39% of gains come from avoided conflicts and 61% from reduced conflict expenditures. |
| Keywords: | contests, conflict resolution, side-payments, experiments |
| JEL: | C72 C91 D72 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:12-01&r=gth |
| By: | Anthony Ziegelmeyer (Max Planck Institute of Economics, Jena); Christoph March (Paris School of Economics); Sebastian Krügel (Max Planck Institute of Economics, Jena, IMPRS "Uncertainty") |
| Abstract: | Weizsäcker (2010) estimates the payoff of actions to test rational expectations and to measure the success of social learning in information cascade experiments. He concludes that participants perform poorly when learning from others and that rational expectations are violated. We show that his estimated payoffs rely on estimates of the publicly known prior and signal qualities which may lead the formulated test of rational expectations to generate false positives. We rely on the true values of the prior and signal qualities to estimate the payoff of actions. We confirm that the rational expectations hypothesis is rejected, but we measure a much larger success of social learning. |
| Keywords: | Information Cascades, Laboratory Experiments, Quantal Response Equilibrium |
| JEL: | C92 D82 |
| Date: | 2012–02–20 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2012-006&r=gth |
| By: | Kenji Fujiwara (School of Economics, Kwansei Gakuin University); Ngo Van Long (Department of Economics, McGill University) |
| Abstract: | Constructing a dynamic game model of trade of an exhaustible resource, this paper compares feedback Nash and Stackelberg equilibria. We consider two dierent leadership scenarios: leadership by the importing country, and leadership by the exporting country. We numerically show that as compared to the Nash equilibrium, both countries are better o if the importing country is a leader, but that the follower becomes worse o if the exporting country is a leader. Consequently, the world welfare is highest under the importing country's leadership and lowest under the exporting country's leadership. |
| Keywords: | dynamic game, feedback Nash equilibrium, feedback Stackelberg equilibrium |
| JEL: | C73 L72 |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:kgu:wpaper:82&r=gth |
| By: | Alcalde, José (Department of Quantitative Methods and Economic Theory); Subiza, Begoña (Department of Quantitative Methods and Economic Theory) |
| Abstract: | This paper proposes a reform for school allocation procedures in order to help integration policies reach their objective. For this purpose, we suggest the use of a natural two-step mechanism. The (equitable) first step is introduced as an adaptation of the deferred-acceptance algorithm designed by Gale and Shapley (1962), when students are divided into two groups. The (efficient) second step captures the idea of exchanging places inherent to Gale’s Top Trading Cycle. This latter step could be useful for Municipal School Boards when implementing some integration policies. |
| Keywords: | Integration Policy; School Allocation; Affirmative Action |
| JEL: | C72 I28 J18 |
| Date: | 2012–02–20 |
| URL: | http://d.repec.org/n?u=RePEc:ris:qmetal:2012_003&r=gth |