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on Game Theory |
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Issue of 2009‒11‒14
fourteen papers chosen by Laszlo A. Koczy Budapest Tech and Maastricht University |
| By: | Johannes Horner (Cowles Foundation, Yale University); Stefano Lovo (HEC School of Management, Paris and GREGHEC); Tristan Tomala (HEC School of Management, Paris and GREGHEC) |
| Abstract: | We characterize belief-free equilibria in infinitely repeated games with incomplete information with N \ge 2 players and arbitrary information structures. This characterization involves a new type of individual rational constraint linking the lowest equilibrium payoffs across players. The characterization is tight: we define a set of payoffs that contains all the belief-free equilibrium payoffs; conversely, any point in the interior of this set is a belief-free equilibrium payoff vector when players are sufficiently patient. Further, we provide necessary conditions and sufficient conditions on the information structure for this set to be non-empty, both for the case of known-own payoffs, and for arbitrary payoffs. |
| Keywords: | Repeated games with incomplete information, Harsanyi doctrine, Belief-free equilibria |
| JEL: | C72 C73 |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1739&r=gth |
| By: | Rida Laraki (Department of Economics, Ecole Polytechnique - CNRS : UMR7176 - Polytechnique - X) |
| Abstract: | Let N be a set of players, C the set of permissible coalitions and G an N-playerstrategic game. A profile is a coalitional-equilibrium if no coalition permissible coalition in C has a unilateral deviation that profits to all its members. Nash-equilibria consider only single player coalitions and Aumann strong-equilibria permit all coalitions to deviate. A new fixed point theorem allows to obtain a condition for the existence of coalitional equilibria that covers Glicksberg for the existence of Nash-equilibria and is related to Ichiishi's condition for the existence of Aumann strong-equilibria. |
| Keywords: | Fixed point theorems, maximum of non-transitive preferences, Nash and strong equilibria, coalitional equilibria |
| Date: | 2009–11–02 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00429293_v1&r=gth |
| By: | László Á. Kóczy (Budapest Tech) |
| Abstract: | We study coalitional games where the proceeds from cooperation depend on the entire coalition structure. The coalition structure core (Kóczy, 2007) is a generalisation of the coalition structure core for such games. We introduce a noncooperative, sequential coalition formation model and show that the set of equilibrium outcomes coincides with the recursive core. In order to extend past results to games that are not totally balanced (understood in this special setting) we introduce subgame-consistency that requires perfectness in relevant subgames only, while subgames that are never reached are ignored. |
| Keywords: | Partition Function, Externalities, Implementation, Recursive Core, Stationary Perfect Equilibrium, Time Consistent Equilibrium |
| JEL: | C71 C72 |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2009.83&r=gth |
| By: | Habis Helga; Herings P. Jean-Jacques (METEOR) |
| Abstract: | We examine the notion of the core when cooperation takes place in a setting with time and uncertainty. We do so in a two-period general equilibrium setting with incomplete markets. Market incompleteness implies that players cannot make all possible binding commitments regarding their actions at different date-events. We unify various treatments of dynamic core concepts existing in the literature. This results in definitions of the Classical Core, the Segregated Core, the Two-stage Core, the Strong Sequential Core, and the Weak Sequential Core. Except for the Classical Core, all these concepts can be defined by requiring absence of blocking in period 0 and at any date-event in period 1. The concepts only differ with respect to the notion of blocking in period 0. To evaluate these concepts, we study three market structures in detail: strongly complete markets, incomplete markets in finance economies, and incomplete markets in settings with multiple commodities. |
| Keywords: | mathematical economics; |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2009026&r=gth |
| By: | Johannes Horner (Cowles Foundation, Yale University); Dinah Rosenberg (Dept. of Economics and Decision Sciences, HEC Paris and GREGHEC); Eilon Solan (School of Mathematical Sciences, Tel Aviv University); Nicolas Vieille (Dept of Economics and Decision Sciences, HEC Paris and GREGHEC) |
| Abstract: | We apply the average cost optimality equation to zero-sum Markov games, by considering a simple game with one-sided incomplete information that generalizes an example of Aumann and Maschler (1995). We determine the value and identify the optimal strategies for a range of parameters. |
| Keywords: | Repeated game with incomplete information, Zero-sum games, Partially observable Markov decision processes |
| JEL: | C72 C73 |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1737&r=gth |
| By: | Alice Becker (Max Planck Institute for Economics, Jena); Tobias Brünner (Goethe University Frankfurt) |
| Abstract: | A unique indivisible commodity with an unknown common value is owned by group of individuals and should be allocated to one of them while compensating the others monetarily. We study the so-called fair division game (Güth, Ivanova-Stenzel, Königstein, and Strobel (2002, 2005)) theoretically and experimentally for the common value case and compare our results to the corresponding common value auction. Whereas symmetric risk neutral Nash equilibria are rather similar for both games, behavior differs strikingly. Implementing auctions and fair division games in the lab in a repeated setting under first- and second-price rule, we find that overall behavior is much more dispersed for the fair division games than for the auctions. Winners' profit margins and shading rates are on average slightly lower for the fair division game. Moreover, we find that behavior in the fair division game separates into extreme over- and underbidding. |
| Keywords: | common value auction, winner's curse, fair division game |
| JEL: | C73 C91 D44 |
| Date: | 2009–11–04 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2009-090&r=gth |
| By: | Heifetz, Aviad (Open University of Israel); Meier, Martin (Instituto de Analisis Economico, CSIC, Barcelona and Institut fur Hohere Studien, Vienna); Schipper, Burkhard C. (University of California, Davis) |
| Abstract: | We define generalized extensive-form games which allow for mutual unawareness of actions. We extend Pearce's (1984) notion of extensive-form (correlated) rationalizability to this setting, explore its properties and prove existence. We define also a new variant of this solution concept, prudent rationalizability, which refines the set of outcomes induced by extensive-form rationalizable strategies. Finally, we define the normal form of a generalized extensive-form game, and characterize in it extensive-form rationalizability by iterative conditional dominance. |
| JEL: | C70 C72 D80 D82 |
| Date: | 2009–05 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:ucdeco:09-10&r=gth |
| By: | Yi-Chun Chen (Dept. of Economics, National University of Singapore); Alfredo Di Tillio (IGIR and Dept. of Economics, Universita Luigi Bocconi); Eduardo Faingold (Cowles Foundation, Yale University); Siyang Xiong (Dept. of Economics, Rice University) |
| Abstract: | We study the robustness of interim correlated rationalizability to perturbations of higher-order beliefs. We introduce a new metric topology on the universal type space, called uniform weak topology, under which two types are close if they have similar first-order beliefs, attach similar probabilities to other players having similar first-order beliefs, and so on, where the degree of similarity is uniform over the levels of the belief hierarchy. This topology generalizes the now classic notion of proximity to common knowledge based on common p-beliefs (Monderer and Samet (1989)). We show that convergence in the uniform weak topology implies convergence in the uniform strategic topology (Dekel, Fudenberg, and Morris (2006)). Moreover, when the limit is a finite type, uniform-weak convergence is also a necessary condition for convergence in the strategic topology. Finally, we show that the set of finite types is nowhere dense under the uniform strategic topology. Thus, our results shed light on the connection between similarity of beliefs and similarity of behaviors in games. |
| Keywords: | Rationalizability, Incomplete information, Higher-order beliefs, Strategic topology, Electronic mail game |
| JEL: | C70 C72 |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1734&r=gth |
| By: | Alex Dickson (Department of Economics, University of Strathclyde); Roger Hartley (Department of Economics, University of Manchester) |
| Abstract: | Bilateral oligopoly is a strategic market game with two commodities, allowing strategic behavior on both sides of the market. When the number of buyers is large, such a game approximates a game of quantity competition played by sellers. We present examples which show that this is not typically a Cournot game. Rather, we introduce an alternative game of quantity competition (the market share game) and, appealing to results in the literature on contests, show that this yields the same equilibria as the many-buyer limit of bilateral oligopoly, under standard assumptions on costs and preferences. We also show that the market share and Cournot games have the same equilibria if and only if the price elasticity of the latter is one. These results lead to necessary and su¢ cient conditions for the Cournot game to be a good approximation to bilateral oligopoly with many buyers and to an ordering of total output when they are not satisfied. |
| Keywords: | Quantity competition, Cournot, strategic foundation, commitment |
| JEL: | C72 D21 D43 |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:str:wpaper:0922&r=gth |
| By: | Nicolas Jacquemet (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris); Robert-Vincent Joule (Laboratoire de Psychologie Sociale - Université de Provence); Stephane Luchini (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - CNRS : UMR6579); Jason Shogren (Departement Economy and Finance, University of Wyoming - University of Wyoming) |
| Abstract: | This paper considers whether earned wealth affects bidding behavior in an induced-value second-price auction. We find people bid more sincerely in the auction with earned wealth given monetary incentives; earned wealth did not induce sincere bidding in hypothetical auctions. |
| Keywords: | Auctions; Demand revelation; Experimental valuation; Hypothetical bias; Earned money |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00429894_v1&r=gth |
| By: | Pierre Dehez; Daniela Tellone |
| Abstract: | A group of firms consider collaborating on a project which requires a combination of elements which are owned by some of them. These elements are nonrival but excludable goods i.e. public goods with exclusion like for instance knowledge, data or informations, patents or copyrights. We address the question of how firms should be compensated for the goods they own. We shown that this problem can be framed as a cost sharing game to which standard allocation rules like the Shapley value, the nucleolus or accountings formulas can be applied and compared. Our analysis is inspired by the need for a cooperation between European chemical firms within the regulation program REACH which requires them to submit by 2018 a detailed analysis of the substances they produce or import. |
| Keywords: | cost sharing, Shapley value, core, nucleolus. |
| JEL: | C71 D46 M41 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:ulp:sbbeta:2009-31&r=gth |
| By: | Amedeo Piolatto (Universidad de Alicante) |
| Abstract: | Thinking of electoral rules, common wisdom suggests that proportional rule is more fair, since all voters are equally represented: at times, it turns out that this is false. I study the formation of both Parliament and Government; for the composition of the former I consider plurality and proportional rule; for the formation of the latter, I assume that parties play a non-cooperative game `a la Rubinstein. I show that, unless parties are impatient to form a Government, proportional electoral rules translate into a more distortive distribution of power among parties than plurality rule; this happens because of the bargaining power of small parties during Government formation. |
| Keywords: | Electoral systems, proportional rule, plurality rule, voters’ representation |
| JEL: | C71 D72 H1 P16 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:ieb:wpaper:2009/10/doc2009-27&r=gth |
| By: | Biung-Ghi Ju (Department of Economics, Korea University); Juan D. Moreno-Ternero (Department of Economic Theory, Universidad de Mˆlaga) |
| Abstract: | We investigate the implications and logical relations between progressivity (a principle of distributive justice) and merging-proofness (a strategic principle) in taxation. By means of two characterization results, we show that these two principles are intimately related, despite their different nature. In particular, we show that, in the presence of continuity and consistency (a widely accepted framework for taxation) progressivity implies merging-proofness and that the converse implication holds if we add an additional strategic principle extending the scope of merging-proofness to a multilateral setting. By considering operators on the space of taxation rules, we also show that progressivity is slightly more robust than merging-proofness. |
| Keywords: | taxation, progressivity, merging-proofness, consistency, operators |
| JEL: | C70 D63 D70 H20 |
| Date: | 2009–11 |
| URL: | http://d.repec.org/n?u=RePEc:mal:wpaper:2009-7&r=gth |
| By: | Simone Borghesi (University of Siena); Angelo Antoci (University of Sassari); Marcello Galeotti (University of Florence) |
| Abstract: | This paper analyses the effects on economic agents' behaviour of an innovative environmental protection mechanism that the Public Administration of a tourist region may adopt to attract visitors while protecting the environment. On the one hand, the Public Administration sells to the tourists an environmental call option that gives them the possibility of being (partially or totally) reimbursed if the environmental quality in the region turns out to be below a given threshold level. On the other hand, it offers the firms that adopt an innovative, non-polluting technology an environmental put option that allows them to get a reimbursement for the additional costs imposed by the new technology if the environmental quality is above the threshold level. The aim of the paper is to study the dynamics that arise with this financial mechanism from the interaction between the economic agents and the Public Administration in an evolutionary game context. |
| Keywords: | Environmental Bonds, Call and Put Options, Technological Innovation, Evolutionary Dynamics |
| JEL: | C73 D62 G10 O30 Q28 |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2009.90&r=gth |