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on Game Theory |
| By: | Yehuda Levy |
| Abstract: | A long-standing open question raised in the seminal paper of Kalai and Lehrer (1993) is whether or not the play of a repeated game, in the rational learning model introduced there, must eventually resemble play of exact equilibria, and not just play of approximate equilibria as demonstrated there. This paper shows that play may remain distant - in fact, mutually singular - from the play of any equilibrium of the repeated game. We further show that the same inaccessibility holds in Bayesian games, where the play of a Bayesian equilibrium may continue to remain distant from the play of any equilibrium of the true game. |
| Keywords: | Rational Learning, Repeated Games, Nash Equilibrium |
| JEL: | C65 C72 C73 |
| Date: | 2014–11–06 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:731&r=gth |
| By: | Ulrich Faigle (Universität zu Köln - Mathematisches Institut); Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris) |
| Abstract: | The Shapley value is defined as the average marginal contribution of a player, taken over all possible ways to form the grand coalition $N$ when one starts from the empty coalition and adds players one by one. The authors have proposed in a previous paper an allocation scheme for a general model of coalition formation where the evolution of the coalition of active players is ruled by a Markov chain, and need not finish at the grand coalition. The aim of this note is to develop some explanations in the general context of time discrete stochastic processes, exhibit new properties of the model, correct some inaccuracies in the original paper, and give a new version of the axiomatization. |
| Keywords: | coalitional game; coalition formation process; Shapley value |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-00912889&r=gth |
| By: | Douglas Davis (Virginia Commonwealth University); Asen Ivanov (Queen Mary University of London); Oleg Korenok (Virginia Commonwealth University) |
| Abstract: | Using a laboratory experiment, we investigate whether a variety of behaviors in repeated games are related to an array of individual characteristics that are popular in economics: risk attitude, time preference, trust, trustworthiness, altruism, strategic skills in one-shot matrix games, compliance with first-order stochastic dominance, ability to plan ahead, and gender. We do find some systematic relationships. A subject's patience, gender, altruism, and compliance with first-order stochastic dominance have some limited systematic effects on her behavior in repeated games. At the level of a pair of subjects who are playing a repeated game, each subject's patience, gender, and ability to choose an available dominant strategy in a one-shot matrix game systematically affect the frequency of the cooperate-cooperate outcome. However, overall, the number of systematic relationships is surprisingly small. |
| Keywords: | Experiment, Repeated game, Individual characteristics |
| JEL: | C91 C92 D03 D70 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp728&r=gth |
| By: | Gaëtan Fournier (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne); Marco Scarsini (Engineering and System Design Pillar - Singapore University of Technology and Design) |
| Abstract: | We consider a Hotelling game where a finite number of retailers choose a location, given that their potential customers are distributed on a network. Retailers do not compete on price but only on location, therefore each consumer shops at the closest store. We show that when the number of retailers is large enough, the game admits a pure Nash equilibrium and we construct it. We then compare the equilibrium cost bore by the consumers with the cost that could be achieved if the retailers followed the dictate of a benevolent planner. We perform this comparison in term of the induced price of anarchy, i.e., the ratio of the worst equilibrium cost and the optimal cost, and the induced price of stability, i.e., the ratio of the best equilibrium cost and the optimal cost. We show that, asymptotically in the number of retailers, these ratios are two and one, respectively. |
| Keywords: | Induced price of anarchy; induced price of stability; location games on networks; pure equilibria; large games |
| Date: | 2014–04 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-00983085&r=gth |
| By: | Ralph-C Bayer (School of Economics, University of Adelaide) |
| Abstract: | A player's knowledge of her own actions and the corresponding own payoffs may enable her to infer or form belief about what the payoffs would have been if she had played differently. In studies of low-information game settings, however, players' ex-post inferences and beliefs have been largely ignored by quantitative learning models. For games with large strategy spaces, the omission may seriously weaken the predictive power of a learning model. We propose an extended payoff assessment learning model which explicitly incorporates players' ex-post inferences and beliefs about the foregone payoffs for unplayed strategies. We use the model to explain the pricing and learning behavior observed in a Bertrand market experiment. Maximum likelihood estimation shows that the extended model organizes the data remarkably well at both aggregate level and individual level. |
| Keywords: | Learning, Ex-Post Inference, Partial Information, Bertrand Duopoly |
| JEL: | C73 D43 D83 L13 |
| Date: | 2013–11 |
| URL: | http://d.repec.org/n?u=RePEc:adl:wpaper:2013-22&r=gth |
| By: | Fehr, Dietmar; Schmid, Julia |
| Abstract: | Contest or auction designers who want to maximize the overall revenue are frequently concerned with a trade-off between contest homogeneity and inclusion of bidders with high valuations. In our experimental study, we find that it is not profitable to exclude the most able bidder in favor of greater homogeneity among the remaining bidders, even if the theoretical exclusion principle predicts otherwise. This is because the strongest bidders considerably overexert. A possible explanation is that these bidders are afraid they will regret a low but risky bid if they lose and thus prefer a strategy which gives them a lower but secure pay-off. |
| Keywords: | experiments,contests,all-pay auction,heterogeneity,regret aversion |
| JEL: | C72 C92 D84 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:wzbmbh:spii2014206&r=gth |
| By: | Nicolas Jacquemet (EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris, BETA - Bureau d'économie théorique et appliquée - CNRS : UMR7522 - Université de Strasbourg - Université Nancy II); Adam Zylbersztejn (EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris, CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne) |
| Abstract: | Experiments based on the Beard and Beil (1994) two-player coordination game robustly show that coordination failures arise as a result of two puzzling behaviors: (i) subjects are not willing to rely on others' self-interested maximization, and (ii) self-interested maximization is not ubiquitous. Such behavior is often considered to challenge the relevance of subgame perfectness as an equilibrium selection criterion, since weakly dominated strategies are actually used. We report on new experiments investigating whether inequality in payoffs between players, maintained in most lab implementations of this game, drives such behavior. Our data clearly show that the failure to maximize personal payoffs, as well as the fear that others might act this way, do not stem from inequality aversion. This result is robust to varying the saliency of decisions, repetition-based learning and cultural differences between France and Poland. |
| Keywords: | Coordination Failure ; Subgame perfectness ; Non-credible threats; Laboratory experiments; Social Preferences; Inequality Aversion |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-01026080&r=gth |
| By: | James Andreoni; Alison Sanchez |
| Abstract: | We study whether actions are justified by beliefs, as is usually assumed, or whether beliefs are justified by actions. In our experiment, subjects participate in a trust game, after which they have an opportunity to state their beliefs about their opponent's actions. Subsequently, subjects participate in a task designed to "reveal" their true beliefs. We find that subjects who make selfish choices and show strategic sophistication falsely state their beliefs in order to project a more favorable social image. By contrast, their "revealed" beliefs were significantly more accurate, which betrayed these subjects as knowing that their selfishness was not justifiable by their opponent's behavior. |
| JEL: | C9 D03 D83 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:20649&r=gth |
| By: | Svetlana Boyarchenko (Department of Economics, University of Texas at Austin); Sergei Levendorskii (Department of Mathematics, University of Leicester) |
| Abstract: | We study a stochastic version of Fudenberg--Tirole's preemption game. Two firms contemplate entering a new market with stochastic demand. Firms differ in sunk costs of entry. If the demand process has no upward jumps, the low cost firm enters first, and the high cost firm follows. If leader's optimization problem has an interior solution, the leader enters at the optimal threshold of a monopolist; otherwise, the leader enters earlier than the monopolist. If the demand admits positive jumps, then the optimal entry threshold of the leader can be lower than the monopolist's threshold even if the solution is interior; simultaneous entry can happen either as an equilibrium or a coordination failure; the high cost firm can become the leader. We characterize subgame perfect equilibrium strategies in terms of stopping times and value functions. Analytical expressions for the value functions and thresholds that define stopping times are derived. |
| Keywords: | stopping time games, preemption, Levy uncertainty |
| JEL: | C73 C61 D81 |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:tex:wpaper:131101&r=gth |
| By: | Fernanda Estevan; Thomas Gall; Patrick Legros; Andrew F. Newman |
| Abstract: | This paper examines possible effects of college admission policy on general equilibrium outcomes at the high school stage. Specifically, we investigate whether a policy that bases college admission on relative performance at high school could modify in the aggregate the degree of segregation in schools, by inducing some students to relocate to schools that offer weaker competition. In a matching model, such high school arbitrage will occur in equilibrium and typically result in desegregating high schools, if schools are segregated with regards to socio-economic characteristics that are correlated with academic performance and race. This is supported by empirical evidence on the effects of the Texas Top Ten Percent Law, indicating that a policy designed to support diversity at the college level in fact achieved high school desegregation, unintentionally generating incentives for some students to choose schools strategically. |
| Keywords: | matching; affirmative action; education; college admission; high school desegregation; Texas Top Ten Percent |
| JEL: | C78 I23 D45 J78 |
| Date: | 2014–11–06 |
| URL: | http://d.repec.org/n?u=RePEc:spa:wpaper:2014wpecon26&r=gth |