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on Game Theory |
| By: | Ziv Hellman |
| Abstract: | This paper is concerned with the question of extending the definition of the bargaining set, a cooperative game solution, when cooperation takes place in a repeated setting. The focus is on situations in which the players face (finite or infinite) sequences of exogenously specified TU-games and receive sequences of imputations against those static cooperative games in each time period. Two alternative definitions of what a `sequence of coalitions' means in such a context are considered, in respect to which the concept of a repeated game bargaining set may be defined, and existence and non-existence results are studied. A solution concept we term subgame-perfect bargaining set sequences is also defined, and sufficient conditions are given for the nonemptiness of subgame-perfect solutions in the case of a finite number of time periods. |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp523&r=gth |
| By: | Lijue Xie (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I); Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I) |
| Abstract: | In the classical setting of cooperative game theory, it is always assumed that all coalitions are feasible. However in many real situations, there are restrictions on the set of coalitions, for example duo to communication, order or hierarchy on the set of players, etc. There are already many works dealing with games on restricted set of coalitions, defining many different structures for the set of feasible coalitions, called set systems. We propose in this paper to consider k-regular set systems, that is, set systems having all maximal chains of the same length k. This is somehow related to communication graphs. We study in this perspective the core of games defined on k-regular set systems. We show that the core may be unbounded and without vertices in some situations. |
| Keywords: | Cooperative game ; feasible coalition ; core |
| Date: | 2009–09 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00423922_v2&r=gth |
| By: | Herings P. Jean-Jacques; Predtetchinski Arkadi (METEOR) |
| Abstract: | We show that in the canonical non-cooperative multilateral bargaining game, a subgameperfect equilibrium exists in pure stationary strategies, even when the space of feasible payoffs is not convex. At such an equilibrium there is no delay. We also have the converse result that randomization will not be used in this environment in the sense that all stationary subgame perfect equilibria do not involve randomization on the equilibrium path. Nevertheless, mixed strategy profiles can lead to Pareto superior payoffs in non-convex cases. |
| Keywords: | operations research and management science; |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2009044&r=gth |
| By: | Philippe Bich (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) |
| Abstract: | In a recent but well known paper, Reny has proved the existence of Nash equilibria for compact and quasiconcave games, with possibly discontinuous payoff functions. In this paper, we prove that the quasiconcavity assumption in Reny's theorem can be weakened : we introduce a measure allowing to localize the lack of quasiconcavity, which allows to refine the analysis of equilibrium existence. |
| Keywords: | Nash equilibrium, discontinuity, quasiconcavity. |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00426402_v1&r=gth |
| By: | Rabia Nessah (IÉSEG School of Management, LEM-CNRS (UMR 8179)); Guoqiang Tian (Texas A&M University, USA) |
| Abstract: | This paper investigates the existence of strong Nashequilibria (SNE) in continuous and convex games. We show that the concavity and an additional condition on payoff functions, together with the compactness of strategy space, permit the existence of strong Nash equilibria. These conditions are satisfied in many economic games and are quite simple to check. We also characterize the existence of SNE by providing a necessary and sufficient condition. Moreover, we suggest a procedure that can be used to efficiently compute strong Nash equilibrium. The result is illustrated with an application to an economy with multilateral environmental externalities and to the simple oligopoly static model. |
| Keywords: | Non cooperative game, strong Nash equilibrium, weak Pareto-efficiency |
| Date: | 2009–04 |
| URL: | http://d.repec.org/n?u=RePEc:ies:wpaper:e200906&r=gth |
| By: | Rabia Nessah (IÉSEG School of Management, LEM-CNRS (UMR 8179)); Guoqiang Tian (Texas A&M University, USA) |
| Abstract: | This paper investigates the existence of pure strategy, dominant-strategy, and mixed strategy Nash equilibria in discontinuous and nonconvex games. We introduce a new notion of very weak continuity, called weak transfer continuity, which holds in a large class of discontinuous economic games and is easy to check. We show that it, together with the compactness of strategy space and the quasiconcavity of payoff functions, permits the existence of pure strategy Nash equilibria. Our equilibrium existence result neither implies nor is implied by the existing results in the literature such as those in Baye et al. [1993] and Reny [1999]. We provide sufficient conditions for weak transfer continuity by introducing notions of weak transfer upper continuity and weak transfer lower continuity. These conditions are satisfied in many economic games and are often quite simple to check. We also introduce the notion of weak dominant transfer upper continuity, and use it to study the existence of dominant strategy equilibria. We then generalize these results and those in Baye et al. [1993] and Reny [1999] without assuming any form of quasi-concavity of payoff functions or convexity of strategy spaces. |
| Keywords: | Nash equilibrium, dominant strategy equilibrium, discontinuity, nonquasiconcavity, nonconvexity and mixed strategy |
| Date: | 2009–04 |
| URL: | http://d.repec.org/n?u=RePEc:ies:wpaper:e200814&r=gth |
| By: | Grigorieva Elena; Herings P. Jean-Jacques; Müller Rudolf; Vermeulen Dries (METEOR) |
| Abstract: | This paper studies the sales of a single indivisible object where bidders have continuous valuations. In Grigorieva et al. [13] it was shown that, in this setting, query auctions necessarily allocate inefficiently in equilibrium. In this paper we propose a new sequential auction, called the c-fraction auction. We show c-fraction auctions guarantee approximate efficiency at any desired level of accuracy, independent of the number of bidders. We discuss the running time and the efficiency in the ex-post equilibrium of the auction. We show that by changing the parameter c of the auction we can trade off efficiency against running time. |
| Keywords: | operations research and management science; |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2009047&r=gth |
| By: | Maroš Servátka (University of Canterbury); Radovan Vadovic |
| Abstract: | Experimental evidence suggests the size of the foregone outside option of the first mover does not affect the behavior of the second mover in the lost wallet game. In this paper we experimentally compare the behavior of subjects when they face an outside option with unequal payoffs, i.e., the first mover gets 10 and the second mover gets 0, and when they face an outside option with equal payoffs, i.e., both get 5. Consistent with the most of the literature we do not find a significant difference in behavior of second movers. |
| Keywords: | Experimental economics; fairness; inequality; lost wallet game; outside option |
| JEL: | C72 C78 C91 |
| Date: | 2009–10–16 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:09/14&r=gth |
| By: | Martin Shubik (Cowles Foundation, Yale University) |
| Abstract: | The El Farol Bar problem with coordination is reconsidered in terms and extended with consideration of further context. |
| Keywords: | Random search context |
| JEL: | C73 D84 |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1733&r=gth |
| By: | Sobbrio, Francesco |
| Abstract: | This paper provides an empirical investigation of electoral participation and communicative voting in 14 European countries. We estimate a multi-level voting process where individuals face a participation decision (whether to vote or abstain) and a voting decision (whether to vote strategically for a likely winner party or as communicating for a sure loser party). Our main findings can be summarized as follows. First, individuals who are either independent or uninformed are less likely to turnout. However, being both independent and uninformed does not have any statistically significant effect on electoral participation. Thus, our results question the empirical relevance of the swing voter's curse theory in large elections. Second, the probability of voting as communicating is positively related with the level of education and the degree of dissatisfaction with the political system. Finally, political preferences and institutional features characterizing the functioning of the political system and of the media market have a significant effect both on electoral participation and on the voting decision. |
| Keywords: | Electoral turnout; Swing Voter's Curse; Communicative voting; Strategic voting; Multi-level qualitative choices |
| JEL: | D72 C25 |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:18216&r=gth |
| By: | Kocher, Martin (Department of Economics, University of Munich,); Martinsson, Peter (Department of Economics, School of Business, Economics and Law, Göteborg University); Visser, Martine (School of Economics, University of Cape Town) |
| Abstract: | Studies have shown that there are differences in cooperative behavior across countries. Furthermore, differences in the use and the reaction on the introduction of a norm enforcement mechansism have been documented in cross-cultural studies, recently. We present data which prove that stark differences in both dimensions can exist even within the same town. For this end, a unique data set was created, based on public goods experiments conducted in South Africa. Most of the group differences can, however, be explained by variables accounting for social capital and social environment, such as trust or household violence.<p> |
| Keywords: | Cooperation; public goods; punishment; experiment; social capital; South Africa |
| JEL: | C72 C91 H41 Z13 |
| Date: | 2009–10–19 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:gunwpe:0385&r=gth |
| By: | Sébastien ROUILLON (GREThA UMR CNRS 5113) |
| Abstract: | This paper presents a new economic mechanism, such that the associated game form implements Lindahl equilibria as Nash equilibria. Each player sends a 2-dimensional message, in order to tell his marginal propensity to pay and his demand for the public good. At a Nash equilibrium, the players directly and honestly reveal data defining a Lindahl equilibrium and the mechanism implements the corresponding allocation. In a quasi-linear economy, formalizing out-of-equilibrium behaviours of the players as a gradient process, the unique stationary point of this process is a Nash equilibrium of the game and it is shown to be globally stable. |
| Keywords: | Public good; Lindalh equilibrium; Economic mechanism |
| JEL: | D70 H41 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:grt:wpegrt:2009-09&r=gth |