
on Game Theory 
By:  Francesco Passarelli (ISLA, Universita' Bocconi, Milano) 
Abstract:  In this paper I explore asymmetric coalitional bargaining. Players are possibly different in preferences and in probability to place threats; the agreements emerge randomly during negotiations. As a result, players negotiate with different degree of enthusiasm. I compute a solution that I call random type value. The random type value is the Shapley value when players have the same ability to place threats, the agreements are equally likely, and, either players have the same (possibly nonlinear) preferences, or players like “in the same way” different agreements. In a pure bargaining game the random type value coincides with the Nash bargaining solution when the threat points and the agreements are uniformly distributed. This suggests that the random type value is well suited to model a broad range of bargaining games in a rich way. I provide two applications: the first one, to political games, where players are distinguishable by their “ideological profiles”; the second one, to incomplete contracts, where, exante, a player can integrate with a partner in order to acquire a bargaining advantage over future trading parties. 
Keywords:  cooperative bargaining, noncooperative bargaining, asymmetric values, political power, contracts 
JEL:  C71 C78 D72 L14 
Date:  2007–01 
URL:  http://d.repec.org/n?u=RePEc:slp:islawp:islawp26&r=gth 
By:  GonzalesAlcon,Carlos; Borm,Peter; Hendrickx,Ruud; Kuijk,Kim van (Tilburg University, Center for Economic Research) 
Abstract:  This paper provides an overview of the various shapes the bestreply multifunctions can take in 2x2x2 trimatrix games. It is shown that, unlike in 2x2 bimatrix games, the best replies to the opponents pure strategies do not completely determine the structure of the Nash equilibrium set. 
Keywords:  noncooperative games;bestreply multifunction;Nash equilibrium 
JEL:  C71 
Date:  2007 
URL:  http://d.repec.org/n?u=RePEc:dgr:kubcen:200711&r=gth 
By:  Régis Breton; Bertrand Gobillard 
Abstract:  We propose an approach to restricting the set of equilibria in a strategic market game and use it to assess the robustness of the price dispersion results obtained by Koutsougeras [2003, J. Econ. Theory 108, 169175] in the multiple trading posts setup. More precisely, we perturb the initial game by the introduction of transaction costs and our main results are the following. (i) No equilibrium with price dispersion of the game with costless transactions can be approached by equilibria with positive transaction costs as costs get arbitrarily small. (ii) When this type of perturbation is considered the set of equilibrium outcomes is not a®ected by the number of trading posts. 
Keywords:  Strategic market games, law of one price, equilibrium selection. 
JEL:  C72 D43 D50 
Date:  2006 
URL:  http://d.repec.org/n?u=RePEc:drm:wpaper:200610&r=gth 
By:  Sergiu Hart; Yosef Rinott; Benjamin Weiss 
Abstract:  An evolutionarily stable strategy (ESS) is an equilibrium strategy that is immune to invasions by rare alternative ("mutant") strategies. Unlike Nash equilibria, ESS do not always exist in finite games. In this paper, we address the question of what happens when the size of the game increases: does an ESS exist for "almost every large" game? Letting the entries in the n x n game matrix be randomly chosen according to an underlying distribution F, we study the number of ESS with support of size 2. In particular, we show that, as n goes to infinity, the probability of having such an ESS: (i) converges to 1 for distributions F with "exponential and faster decreasing tails" (e.g., uniform, normal, exponential); and (ii) it converges to 1  1/sqrt(e) for distributions F with "slower than exponential decreasing tails" (e.g., lognormal, Pareto, Cauchy). Our results also imply that the expected number of vertices of the convex hull of n random points in the plane converges to infinity for the distributions in (i), and to 4 for the distributions in (ii). 
Date:  2007–01 
URL:  http://d.repec.org/n?u=RePEc:huj:dispap:dp445&r=gth 
By:  Fabien Lange (Centre d'Economie de la Sorbonne); Michel Grabisch (Centre d'Economie de la Sorbonne) 
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, probalistic efficient values, regular values, Kirchhoff's laws. 
JEL:  C71 
Date:  2006–12 
URL:  http://d.repec.org/n?u=RePEc:mse:wpsorb:b06087&r=gth 
By:  Petra Huck (Environmental Economics and Agricultural Policy Group, Technical University of Munich) 
Abstract:  Differential games link strategic interactions between agents and optimization concerning time. Past and current actions of each player influence all future strategy sets and pay offs through a transition law. Due to high complexity, it is hard to find a Nashequilibrium within a differential game and it is even harder to get some results in comparative statics. It is the purpose of the paper to describe an approximation routine for an openloop Nash equilibrium of a simple differential game in exhaustible resources. Excel is applied as it is a wild spread tool. 
JEL:  A22 C73 Q30 
Date:  2005–04 
URL:  http://d.repec.org/n?u=RePEc:tuu:papers:042005&r=gth 
By:  Camille Chaserant 
Abstract:  Social identity, or group membership, affects economic outcomes. However, this influence may differ according to the nature of the groups involved. Investigating the weakest group cohesion necessary to influence individual behaviors, we undertook three linked ultimatum game experiments involving a minimal categorization process. Three main results are presented here: (i) Belonging to a minimal group affects behaviors; (ii) Men and women differ systematically in the nature of this influence and (iii) The ‘label’ given to a minimal group is in itself not neutral. 
Keywords:  Minimal group, ultimatum game, social identity, gender 
JEL:  C91 A12 C99 
Date:  2006 
URL:  http://d.repec.org/n?u=RePEc:drm:wpaper:200613&r=gth 
By:  Petra Huck (Environmental Economics and Agricultural Policy Group, Technical University of Munich) 
Abstract:  Differential games combine strategic interactions between agents and optimization concerning time. Decisions made in the past determine the present and even the future .in pay off as well as in the opportunities available . for oneself and for the rival players, eventually too. Unfortunately, due to high complexity it is hard to find a Nashequilibrium within a differential game and it is even harder to get some results in comparative statics. It is the purpose of the paper at hand to present findings concerning comparative statics in a differential game discussed by Wacker and Blank (1999). Comparative statics become available due to a routine solving for the openloop Nash equilibrium for each parameter combination under consideration. A description of the routine . a 4 step simulation run which approximates the equilibrium numerically . was presented in an earlier Working Paper. In the earlier Paper Excel was applied as it is a wild spread tool. Here again Excel, its Solver and Macros constitute the main instruments; they are used to get repeated simulation runs for varying parameter constellations. The findings presented here concern varying allocations in initial stocks. Generalization to comparative statics in further parameters is in progress. 
JEL:  A22 C73 Q30 
Date:  2005–05 
URL:  http://d.repec.org/n?u=RePEc:tuu:papers:052005&r=gth 
By:  Kendra N. McLeish (University of Calgary); Robert J. Oxoby (University of Calgary and IZA) 
Abstract:  Among economists, there is increased recognition of the role individuals’ identities play in decisionmaking. In this paper, we conduct laboratory experiments in which we explore the motivations for and the effects of group identity. We find that negative outgroup opinion (acting as an intergroup identity threat) can motivate ingroup/outgroup effects in a simple bargaining context. Further, our results suggest that disparagement of group norms by members of the ingroup (acting as an intragroup identity threat) increases the use of costly punishment within the ingroup. 
Keywords:  identity, fairness, reciprocity, experiments 
JEL:  C9 D1 M5 
Date:  2007–01 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp2572&r=gth 
By:  Zhou,Jun (Tilburg University, Center for Economic Research) 
Abstract:  This paper studies the consequences of asymmetric litigation costs. Under three different protocols: static legal process, dynamic legal process with exogenous sequencing and dynamic legal process with endogenous sequencing, solutions are obtained for the litigation e®orts and the expected value of lawsuits on each side. Outcomes are evaluated in terms of two normative criteria: achieving `justice' and minimizing aggregate litigation cost. The theory implies that a moderate degree of asymmetry may improve access to justice. The dynamics of legal process may accentuate or diminish the e®ect of asymmetry. The endogenous sequencing protocol minimizes cost and may improve access to justice. 
Keywords:  access to justice;endogenous sequencing;dynamics of litigation process; resource dissipation 
JEL:  C72 D63 D72 K41 
Date:  2007 
URL:  http://d.repec.org/n?u=RePEc:dgr:kubcen:200710&r=gth 
By:  Thibault Gajdos (Centre d'Economie de la Sorbonne); Takashi Hayashi (University of Texas); JeanMarc Tallon (Centre d'Economie de la Sorbonne); JeanChristophe Vergnaud (Centre d'Economie de la Sorbonne) 
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 probabilitypossibility 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 probabilitypossibility set and f is an act mapping states into outcomes. The representation result delivers multiplepriors utility at each probabilitypossibility set. There is a mapping that gives for each probabilitypossibility 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 probabilitypossibility 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 probabilitypossibility set and (ii) shrinking the probabilitypossibility set toward the mean value to a degree determined by preference. 
Keywords:  Imprecise information, imprecision aversion, multiple priors, Steiner point. 
JEL:  D81 
Date:  2006–07 
URL:  http://d.repec.org/n?u=RePEc:mse:wpsorb:v06081&r=gth 
By:  Pierre, DEHEZ (UNIVERSITE CATHOLIQUE DE LOUVAIN, Department of Economics) 
Abstract:  The cost sharing rule derived from the Shapley value is the unique sharing rule which allocates fixed costs uniformly 
Keywords:  Cost sharing, Value, Fixed cost 
JEL:  C71 D46 
Date:  2006–12–15 
URL:  http://d.repec.org/n?u=RePEc:ctl:louvec:2006064&r=gth 