|
on Game Theory |
| By: | Sergio Puente (Banco de España) |
| Abstract: | A concept of dynamic stability in infinitely repeated games with discounting is presented. For this purpose, one modification of the available theory is needed: we need to relax the assumption that the game starts in a given period. Under this new framework, we propose stable strategies such that a folk theorem with an additional stability requirement still holds. Under these strategies, convergence to the long run outcome is achieved in a finite number of periods, no matter what actions or deviations have been played in the past. Hence, we suggest a way in which a player can build up his reputation after a deviation. |
| Keywords: | repeated games, stability, stable strategies |
| JEL: | C70 C72 |
| Date: | 2006–08 |
| URL: | http://d.repec.org/n?u=RePEc:bde:wpaper:0618&r=gth |
| By: | Yi-Chun Chen; Ngo Van Long; Xiao Luo |
| Abstract: | We offer a definition of iterated elimination of strictly dominated strategies (IESDS) for games with (in)finite players, (non)compact strategy sets, and (dis)continuous payoff functions. IESDS is always a well-defined order independent procedure that can be used to solve Nash equilibrium in dominance-solvable games. We characterize IESDS by means of a "stability" criterion, and offer a sufficient and necessary epistemic condition for IESDS. We show by an example that IESDS may generate spurious Nash equilibria in the class of Reny's better-reply secure games. We provide sufficient/necessary conditions under which IESDS preserves the set of Nash equilibria. <P>Nous donnons une définition de l’élimination itérative des stratégies qui sont strictement donimées (EISSD) pour les jeux avec un nombre fini (ou infini) de joueurs , des ensembles de stratégies compactes (ou non-compactes), et des fonctions de gains continues (ou non-continues). Le processus EISSD est bien défini et indépendant de l’ordre d’élimination. Nous donnons une caractérisation du processus EISSD en utilisant un critère de stabilité et offrons une condition épistémologique. Nous démontrons que le processus EISSD peut produire des équilibres faux dans la classe des jeux de meilleures réponses sécuritaires de Reny. Nous donnons des conditions nécessaires et suffisantes pour que le processus EISSD conserve l’ensemble des équilibre de Nash. |
| Keywords: | game theory, strict dominance, iterated elimination, Nash equilibrium, Reny's better-reply secure games., théorie des jeux, dominance stricte, élimination itérative, équilibre de Nash, jeux de meilleures réponses sécuritaires de Reny |
| JEL: | C70 C72 |
| Date: | 2007–02–01 |
| URL: | http://d.repec.org/n?u=RePEc:cir:cirwor:2007s-03&r=gth |
| By: | Geoffroy de Clippel; Roberto Serrano |
| Abstract: | Our concern is the extension of the theory of the Shapley value to games with externalities. Using the standard axiom systems behind the Shapley value for an arbitrary exogenous coalition structure leads to the identification of bounds on players’ payoffs around an \"externality-free\" value. In endogenizing the coalition structure, we analyze a two-stage process of coalition formation in whose second stage our axiomatic results are applied. We find reasons to explain inefficient coalition structures, and provide sufficient conditions for efficiency. |
| Keywords: | externalities; marginal contributions; Shapley value; Pigouvian transfers; coalition formation |
| JEL: | C7 D62 |
| Date: | 2007–02–28 |
| URL: | http://d.repec.org/n?u=RePEc:imd:wpaper:wp2007-04&r=gth |
| By: | Anirban Kar (University of Warwick); Indrajit Ray (University of Birmingham); Roberto Serrano (Brown University) |
| Abstract: | We view achieving a particular correlated equilibrium distribution for a normal form game as an implementation problem. We show, using a parametric version of the two-person Chicken game and a wide class of correlated equilibrium distributions, that a social choice function that chooses a particular correlated equilibrium distribution from this class does not satisfy the Maskin monotonicity condition and therefore can not be fully implemented in Nash equilibrium. |
| Keywords: | correlated equilibrium distribution; implementation; monotonicity |
| JEL: | C72 |
| Date: | 2007–02–28 |
| URL: | http://d.repec.org/n?u=RePEc:imd:wpaper:wp2007-03&r=gth |
| By: | Fabien Lange (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 cooperative game theory, the Shapley value is a central notion defining a rational way to share the total worth of a game among players. In this paper, we address a general framework, namely regular set systems, where the set of feasible coalitions forms a poset where all maximal chains have the same length. We first show that previous definitions and axiomatizations of the Shaphey value proposed by Faigle and Kern and Bilbao and Edelman still work. our main contribution is then to propose a new axiomatization avoiding the hierarchical strength axiom of Faigle and Kern, and considering a new way to define the symmetry among players. Borrowing ideas from electric networks theory, we show that our symmetry axiom and the classical efficiency axiom correspond actually to the two Kirchhoff's laws in the resistor circuit associated to the Hasse diagram of feasible coalitions. We finally work out a weak form of the monotonicity axiom which is satisfied by the proposed value. |
| Keywords: | Regular set systems, regular games, Shapley value, probabilistic efficient values, regular values, Kirchhoff's laws. |
| Date: | 2007–02–12 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00130449_v1&r=gth |
| By: | Andersson , Ola (Department of Economics, Lund University); Wengström, Erik (Department of Economics, Lund University) |
| Abstract: | In this paper we experimentally investigate cooperation and non-binding communication in a two-stage game. The game has a subgame perfect equilibrium where subjects can sustain cooperation in the first stage by threatening to punish deviant behavior in the second stage. In contrast, renegotiation-proofness rules out cooperation in the first stage when intra-play communication is possible. Our results provide some support for this argument. We observe less cooperation in the first stage when intra-play communication is possible. Moreover, pre-play communication only has a significant impact on actions when intra-play communication is not allowed. The experimental design also enables us to perform an in-depth analysis of communication. |
| Keywords: | Renegotiation; Communication; Cooperation; Experiments |
| JEL: | C72 C92 |
| Date: | 2007–02–21 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:lunewp:2007_004&r=gth |
| By: | Mumcu, Ayse; Saglam, Ismail |
| Abstract: | In this paper, we introduce interdependent preferences to a classical one-to-one matching problem that allows for the prospect of being single, and study the existence and properties of stable matchings. We obtain the relationship between the stable set, the core, and the Pareto set, and give a sufficiency result for the existence of the stable set and the core. We also present several findings on the issues of gender optimality, lattices, strategy-proofness, and rationalizability. |
| Keywords: | One-to-one matching; externalities |
| JEL: | D62 C71 C78 |
| Date: | 2006–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:1908&r=gth |
| By: | Mumcu, Ayse; Saglam, Ismail |
| Abstract: | In this paper, we model college admissions under early decision in a many-to-one matching framework with two periods. We show that there exists no stable matching system, involving an early decision matching rule and a regular decision matching rule, which is nonmanipulable via early decision quotas by colleges or via early decision preferences by colleges or students. We then analyze the Nash equilibria of the game, in which the preferences of colleges and students in each period are common knowledge and every college determines a quota for the early decision period given its total capacity for the two periods. Under college-optimal and student-optimal matching systems, we show that a pure strategy equilibrium may not exist. However, when colleges or students have common preferences over the other set of agents, 'terminating early decision program' becomes a weakly dominant strategy for each college if every student, choosing to act early, always applies early to his or her top choice college. |
| Keywords: | Many-to-one matching; college admissions; early decision |
| JEL: | C71 C78 |
| Date: | 2007–01–25 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:1906&r=gth |
| By: | Roberto Serrano (Brown University) |
| Abstract: | This article is a brief survey on the Nash program for coalitional games. Results of noncooperative implementation of the Nash solution, the Shapley value and the core are discussed. |
| JEL: | C7 |
| Date: | 2007–02–28 |
| URL: | http://d.repec.org/n?u=RePEc:imd:wpaper:wp2007-05&r=gth |
| By: | Roberto Serrano (Brown University) |
| Abstract: | This article is a survey on bargaining theory. The focus is the game theoretic approach to bargaining, both on its axiomatic and strategic counterparts. The application of bargaining theory to large markets and its connections with competitive allocations are also discussed. |
| JEL: | C7 |
| Date: | 2007–02–28 |
| URL: | http://d.repec.org/n?u=RePEc:imd:wpaper:wp2007-06&r=gth |
| By: | Martin G. Kocher (Universiteit van Amsterdam); Matthias Sutter (University of Innsbruck); Florian Wakolbinger (University of Innsbruck) |
| Abstract: | We study the impact of advice or observation on the depth of reasoning in an experimental beauty-contest game. Both sources of information trigger faster convergence to the equilibrium. Yet, we find that subjects who receive naïve advice outperform uninformed subjects permanently, whereas subjects who observe others’ past behavior before making their decision do only have a temporary advantage over uninformed subjects. We show in a simulation that the latter result is due to subjects failing to make the most out of observing others. |
| Keywords: | social learning; advice; observational learning; beauty-contest game |
| JEL: | C70 C72 C91 |
| Date: | 2007–01–29 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20070015&r=gth |
| By: | Mumcu, Ayse; Saglam, Ismail |
| Abstract: | We study the problem of marriage formation and marital distribution in a two-period model of matching, extending the matching with bargaining framework of Crawford and Rochford (1986). We run simulations to find the effects of alimony rate, legal cost of divorce, initial endowments, couple and single productivity parameters on the payoffs and marital status in the society. |
| Keywords: | Matching; bargaining; marriage; divorce |
| JEL: | C78 J12 |
| Date: | 2006–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:1907&r=gth |
| By: | Thibault Gajdos (CES - Centre d'économie de la Sorbonne - [CNRS : UMR8174] - [Université Panthéon-Sorbonne - Paris I]); Takashi Hayashi (Department of Economics, University of Texas - [University of Texas at Austin]); Jean-Marc Tallon (CES - Centre d'économie de la Sorbonne - [CNRS : UMR8174] - [Université Panthéon-Sorbonne - Paris I]); Jean-Christophe Vergnaud (CES - Centre d'économie de la Sorbonne - [CNRS : UMR8174] - [Université Panthéon-Sorbonne - Paris I]) |
| Abstract: | This paper presents an axiomatic model of decision making which incorporates objective but imprecise information. We axiomatize a decision criterion of the multiple priors (or maxmin expected utility) type. The model achieves two primary objectives. First, it explains how subjective belief varies with information. Second, it identifies an explicit attitude toward imprecision that underlies usual hedging axioms. Information is assumed to take the form of a probability-possibility set, that is, a set P of probability measures on the state space. The decision maker is told that the true probability law lies in P. She is assumed to rank pairs of the form (P,f) where P is a probability-possibility set and f is an act mapping states into outcomes. The representation result delivers multiple-priors utility at each probability-possibility set. There is a mapping that gives for each probability-possibility set the subjective set of priors. This allows both subjective expected utility when the subjective set of priors is reduced to a singleton and the other extreme where the decision maker takes the worst case scenario in the entire probability-possibility set. We show that the relation «more averse to imprecision» is characterized by inclusion of the sets of priors, irrespective of the utility functions that capture risk attitude. We characterize, under extra axioms, a more precise functional form, in which the subjective set of priors is obtained by (i) solving for the «mean value» of the probability-possibility set and (ii) shrinking the probability-possibility set toward the mean value to a degree determined by preference. |
| Keywords: | Imprecise information, imprecision aversion, multiple priors, Steiner point. |
| Date: | 2007–02–09 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00130179_v1&r=gth |
| By: | Andersson , Tommy (Department of Economics, Lund University); Svensson, Lars-Gunnar (Department of Economics, Lund University) |
| Abstract: | This paper considers a fair division problem with two types of indivisible objects, like jobs, houses etc., and one divisible good (money). Each individual consumes exactly one object and some money. It is assumed that the money that associated with each object cannot fall short of an exogenously given level. In order to guarantee existence, the concept of fairness is extended, and we define a new concept of fairness, called weak fairness. The class of weakly fair allocation rules that are coalitionally strategy-proof is characterized. It turns out that a weakly fair allocation rule is coalitionally strategy-proof if and only if it is optimal, where optimality means it must maximize the use of money subject to some upper quantity bounds. |
| Keywords: | Indivisibles; fairness; weak fairness; strategy-proofness |
| JEL: | C71 C78 D63 D71 D78 |
| Date: | 2007–02–21 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:lunewp:2007_003&r=gth |
| By: | Anke Gerber (agerber@isb.unizh.ch); Philipp C. Wichardt (University of Bonn, Department of Economics, Econ. Theory III, Adenauerallee 24-42, 53113 Bonn, Germany. philipp.wichardt@uni-bonn.de.) |
| Abstract: | This paper proposes a simple mechanism aimed to establish positive contributions to public goods in the absence of powerful institutions to sanction free-riders. The idea of the mechanism is to require players to commit to the public good by paying a deposit prior to the contribution stage. If all players commit in this way, those players who do not contribute their share to the public good forfeit their deposit. If there is no universal commitment, all deposits are refunded and the standard game is played. Given deposits are sufficiently high, prior commitment and full ex post contributions are part of a strict subgame perfect Nash equilibrium for the resulting game. As the mechanism obviates the need for any ex post prosecution of free-riders, it is particularly suited for situations where players do not submit to a common authority as in the case of international agreements. |
| Keywords: | public goods, cooperation, institutions, Climate-Change Treaties |
| JEL: | C72 D61 |
| Date: | 2007–02 |
| URL: | http://d.repec.org/n?u=RePEc:trf:wpaper:194&r=gth |
| By: | Harbord, David |
| Abstract: | We revisit Greif's (1993) analysis of trade between the 11th-century Maghribi traders and present two different models which bring into play, in an essential way, historical features of the Maghribi's organization which had no role in Greif's own analysis. Our reformulation of the Maghribi's "punishment strategies" incorporates principal components of their actual historical practice and explains why they may have been necessary to sustain cooperation, especially in the presence of uncertainty or imperfect information. We also model "formal friendships," or trade through bilateral and multilateral partnerships, and predict the Maghribi's practice of providing agency services without pecuniary compensation. We are thus able to provide a richer and more accurate picture of how that organization facilitated trade between widely-dispersed traders in the absence of a reliable legal system to enforce merchant contracts. |
| Keywords: | cooperation; enforcement; trade; institutions |
| JEL: | J41 N75 C72 D23 |
| Date: | 2006–11–08 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:1889&r=gth |