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on Game Theory |
| By: | V. Bhaskar (Department of Economics, University College London); George J. Mailath (Department of Economics, University of Pennsylvania); Stephen Morris (Department of Economics, Princeton University) |
| Abstract: | This paper investigates the Harsanyi (1973)-purifiability of mixed strategies in the repeated prisoners’ dilemma with perfect monitoring. We perturb the game so that in each period, a player receives a private payoff shock which is independently and identically distributed across players and periods. We focus on the purifiability of one-period memory mixed strategy equilibria used by Ely and Välimäki (2002) in their study of the repeated prisoners’ dilemma with private monitoring. We find that any such strategy profile is not the limit of one-period memory equilibrium strategy profiles of the perturbed game, for almost all noise distributions. However, if we allow infinite memory strategies in the perturbed game, then any completely-mixed equilibrium is purifiable. |
| Keywords: | Purification, belief-free equilibria, repeated games |
| JEL: | C72 C73 |
| Date: | 2006–07–13 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:07-024&r=gth |
| By: | Julio Gonzalez-Diaz; Miguel Melendez-Jimenez |
| Abstract: | Often, perfect bayesian equilibrium is loosely defined by stating that players should be sequentially rational given some beliefs in which Bayes rule is applied “whenever possible”. We show that there are games in which it is not clear what “whenever possible” means. Then, we provide a simple definition of perfect bayesian equilibrium for general extensive games that refines both weak perfect equilibrium and subgame perfect equilibrium. |
| Keywords: | non-cooperative game theory, equilibrium concepts, perfect bayesian, Bayes rule. |
| JEL: | C72 |
| Date: | 2007–06 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1446&r=gth |
| By: | Antonio Cabrales (Universidad Carlos III de Madrid); Roberto Serrano (Brown University & IMDEA) |
| Abstract: | We study the classic implementation problem under the behavioral assumption that agents myopically adjust their actions in the direction of better-responses within a given institution. We offer results both under complete and incomplete information. First, we show that a necessary condition for assymptotically stable implementation is a small variation of (Maskin) monotonicity, which we call quasimonotonicity. Under standard assumptions in economic environments, we also provide a mechanism for Nash implementation which has good dynamic properties if the rule is quasimonotonic. Thus, quasimonotonicity is both necessary and almost sufficient for assymptotically stable implementation. Under incomplete information, incentive compatibility is necessary for any kind of stable implementation in our sense, while Bayesian quasimonotonicity is necessary for assymptotically stable implementation. Both conditions are also essentially sufficient for assymptotically stable implementation. We then tighten the assumptions on preferences and mutation processes and provide mechanisms for stochastically stable implementation under more permissive conditions on social choice rules. |
| Keywords: | implementation; bounded rationality; evolutionary dynamics; mechanisms |
| JEL: | C72 D70 D78 |
| Date: | 2007–08–22 |
| URL: | http://d.repec.org/n?u=RePEc:imd:wpaper:wp2007-16&r=gth |
| By: | Marco Battaglini; Thomas Palfrey |
| Abstract: | We study dynamic committee bargaining over an infinite horizon with discounting. In each period a committee proposal is generated by a random recognition rule, the committee chooses between the proposal and a status quo by majority rule, and the voting outcome in period t becomes the status quo in period t+1. We study symmetric Markov equilibria of the resulting game and conduct an experiment to test hypotheses generated by the theory for pure distributional (divide-the-dollar) environments. In particular, we investigate the effects of concavity in the utility functions, the existence of a Condorcet winning alternative, and the discount factor (committee "impatience"). We report several new findings. Voting behavior is selfish and myopic. Status quo outcomes have great inertia. There are strong treatment effects, that are in the direction predicted by the Markov equilibrium. We find significant evidence of concave utility functions. |
| Keywords: | Dynamic bargaining, voting, experiments, divide-the-dollar,committees |
| JEL: | D71 D72 C78 C92 |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1451&r=gth |
| By: | Gabriele Camera; Marco Casari |
| Abstract: | We study the emergence of norms of cooperation in experimental economies populated by strangers interacting indefinitely and lacking formal enforcement institutions. In all treatments the efficient outcome is sustainable as an equilibrium. We address the following questions: can these economies achieve full efficiency? Which institutions for monitoring and enforcement promote cooperation? Finally, what classes of strategies are employed to achieve high efficiency? We find that, first, cooperation can be sustained even in anonymous settings; second, some type of monitoring and punishment institutions significantly promote cooperation; and, third, subjects dislike indiscriminate strategies and prefer selective strategies. |
| Keywords: | experiments, repeated games, cooperation, equilibrium selection, prisoners’ dilemma, random matching |
| JEL: | C70 C92 D44 D51 |
| Date: | 2007–06 |
| URL: | http://d.repec.org/n?u=RePEc:pur:prukra:1201&r=gth |
| By: | Christian Fahrholz (School of Business and Economics, Friedrich-Schiller University Jena, Germany.) |
| Abstract: | Following entrance into the European Union, Central Eastern European Countries (CEECs) are expected to join the European Monetary Union (EMU). These countries may incur considerable costs over the course of their passing through the required Exchange Rate Mechanism II (ERM-II). However, with enough bargaining leverage CEECs may be able to pass some of these costs on to current EMU-members. In turn, a CEEC's leverage depends on their ability to wield successful brinkmanship via an exchange-rate policy characterized by a 'threaten-thy-neighbor' strategy. A two-stage Nash-threat game captures the essentials of the CEECs' phase of ERM-II pass through. |
| Keywords: | Threat game, Nash-bargaining solution, exchange-rate policy, EU-enlargement, EMU |
| JEL: | C72 C78 F33 F51 |
| Date: | 2007–08–22 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2007-050&r=gth |
| By: | Müller Rudolf; Perea Andrés; Wolf Sascha (METEOR) |
| Abstract: | This paper is concerned with a combinatorial, multi-attribute procurement mechanism called combinatorial scoring auction. In the setting that we analyze, private information of the suppliers is multi-dimensional. The buyer wants to procure several items at once. Subsets of these items are characterized by a price as well as by a number of non-monetary attributes called quality (e.g. completion time). The suppliers submit offers specifying prices and quality levels for these subsets. These offers are evaluated according to a quasilinear scoring rule. Based on the resulting scores suppliers win contracts for the delivery of certain items. Such a contract only specifies the set of items a supplier has to deliver and a score that he has to meet. The decision about the specific price-quality combination yielding this contracted score is at the discretion of the supplier who aims at optimizing his own profit. We analyze the equilibria in such auctions and show the link between combinatorial scoring auctions and combinatorial price-only auctions. We demonstrate how this link can be used to employ preexisting knowledge about the equilibrium behavior in regular price-only auctions in the strategic analysis of combinatorial scoring auctions. Our results are the multi-item extension to the results of Asker and Cantillon (2007). |
| Keywords: | mathematical economics; |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2007020&r=gth |
| By: | Grigorieva Elena; Herings P. Jean-Jacques; Müller Rudolf; Vermeulen Dries (METEOR) |
| Abstract: | We investigate the algorithmic performance of Vickrey-Clarke-Groves mechanisms in the single item case. We provide a formal definition of a Vickrey algorithm for this framework, and give a number of examples of Vickrey algorithms. We consider three performance criteria, one corresponding to a Pareto criterion, one corresponding to worst case analysis, and a third criterion related to first-order stochastic dominance. We show that Pareto optimal Vickrey algorithms do not exist and that worst case analysis is of no use in discriminating between Vickrey algorithms. For the case of two bidders, we show the bisection auction to be optimal according to the third criterion. The bisection auction istherefore optimal in a very strong sense. |
| Keywords: | operations research and management science; |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2007013&r=gth |
| By: | Yakov Babichenko |
| Date: | 2007–08–10 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:843644000000000369&r=gth |
| By: | Östling, Robert (Dept. of Economics, Stockholm School of Economics); Wang, Joseph Tao-yi (Department of Economics, National Taiwan University); Chou, Eileen (Management and Organization, Kellogg School of Management, Northwestern University); Camerer, Colin F. (Division for the Humanities and Social Sciences, California Institute of Technology) |
| Abstract: | In the lowest unique positive integer (LUPI) game, players pick positive integers and the player who chose the lowest unique number (not chosen by anyone else) wins a fixed prize. We derive theoretical equilibrium predictions, assuming fully rational players with Poisson-distributed uncertainty about the number of players. We also derive predictions for boundedly rational players using quantal response equilibrium and a cognitive hierarchy of rationality steps with quantal responses. The theoretical predictions are tested using both field data from a Swedish gambling company, and laboratory data from a scaled-down version of the field game. The field and lab data show similar patterns: in early rounds, players choose very low and very high numbers too often, and avoid focal ("round") numbers. However, there is some learning and a surprising degree of convergence toward equilibrium. The cognitive hierarchy model with quantal responses can account for the basic discrepancies between the equilibrium prediction and the data. |
| Keywords: | Population uncertainty; Poisson game; QRE; congestion game; guessing game; experimental methods; behavioral game theory; cognitive hierarchy |
| JEL: | C72 C92 C93 L83 |
| Date: | 2007–08–14 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:hastef:0671&r=gth |
| By: | Fernando Aguiar (IESA-CSIC); Pablo Branas-Garza (Departamento de Teoria Economica, Universidad de Granada); Luis M. Miller (IESA-CSIC; Strategic Interaction Group, Max Planck Institute of Economics) |
| Abstract: | We perform an experimenta linvestigation using a dictator game in which individuals must make a moral decision - to give or not to give an amount of money to poor people in the Third World. A questionnaire in which the subjects are asked about the reasons for their decision shows that, at least in this case, moral motivations carry a heavy weight in the decision: the majority of dictators give the money for reasons of a consequentialist nature. Based on the results presented here and of other analogous experiments, we conclude that dicator behavior can be understood in terms of moral distance rather than social distance and that it systematically deviates from the egoism assumption in economic models and game theory. |
| Keywords: | Keywords: Dictator game, moral distance, moral motivations, experimental economics. |
| JEL: | A13 C72 C91 |
| Date: | 2007–08–20 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2007-047&r=gth |
| By: | IVALDI, Marc; MOTIS, Jrissy |
| JEL: | C14 G14 G34 L10 L20 |
| Date: | 2007–04 |
| URL: | http://d.repec.org/n?u=RePEc:ide:wpaper:7217&r=gth |