
on Game Theory 
By:  Habis Helga; Herings P. JeanJacques (METEOR) 
Abstract:  We introduce the concept of a transferable utility game with uncertainty (TUUgame). In a TUUgame there is uncertainty regarding the payoffs of coalitions. One out of a finite number of states of nature may materialize and conditional on the state, the players are involved in a particular transferable utility game. We consider the case without ex ante commitment possibilities and propose the Weak Sequential Core as a solution concept. We characterize the Weak Sequential Core and show that it is nonempty if all ex post TUgames are convex. We study bankruptcy games with uncertainty and apply the Weak Sequential Core. We find that most of the bestknown allocation rules are unstable in this setting, except for the Constrained Equal Awards rule. 
Keywords:  microeconomics ; 
Date:  2010 
URL:  http://d.repec.org/n?u=RePEc:dgr:umamet:2010038&r=gth 
By:  C. D. Aliprantis; I. Topolyan 
Abstract:  This paper discusses the problem of stability of equilibrium points in normal form games in the tremlinghand framework. An equilibrium point is called perffect if it is stable against at least one seqence of trembles approaching zero. A strictly perfect equilibrium point is stable against every such sequence. We give a sufficient condition for a Nash equilibrium point to be strictly perfect in terms of the primitive characteristics of the game (payoffs and strategies), which is new and not known in the literature. In particular, we show that continuity of the best response correspondence (which can be stated in terms of the primitives of the game) implies strict perfectness; we prove a number of other useful theorems regarding the structure of best responce correspondence in normal form games. 
Keywords:  Strictly perfect equilibrium, best responce correspondence, unit simplex, face of a unit simplex 
JEL:  C7 
Date:  2009–08 
URL:  http://d.repec.org/n?u=RePEc:pur:prukra:1224&r=gth 
By:  I. Topolyan 
Abstract:  We formulate and prove a modification of EilenbergMontgomery fixedpoint theorem, which is a generalization of Kakutani’s theorem. It enables us to provide a direct proof of the existence of perfect equilibria in finite normal form games and extensive games with perfect recall. We construct a correspondence whose fixed points are precisely the perfect equilibria of a given finite game. Existence of a fixed point is secured by the modified version of EilenbergMontgomery theorem. 
Keywords:  Perfect equilibrium, best response correspondence, unit simplex, absolute neighborhood retract, deformation retract, fixed point 
JEL:  C7 
Date:  2009–10 
URL:  http://d.repec.org/n?u=RePEc:pur:prukra:1226&r=gth 
By:  Ezra Einy (Department of Economics, BenGurion University of the Negev, Israel); Ori Haimanko (Department of Economics, BenGurion University of the Negev, Israel) 
Abstract:  We show that the ShapleyShubik power index on the domain of simple (voting) games can be uniquely characterized without the e¢ ciency axiom. In our axiomatization, the efficiency is replaced by the following weaker require ment that we term the gainloss axiom: any gain in power by a player implies a loss for someone else (the axiom does not specify the extent of the loss). The rest of our axioms are standard: transfer (which is the version of additivity adapted for simple games), symmetry or equal treatment, and dummy 
Keywords:  Simple Games, ShapleyShubik Power Index, Effciency Axiom 
JEL:  C71 D72 
Date:  2010 
URL:  http://d.repec.org/n?u=RePEc:bgu:wpaper:1004&r=gth 
By:  Susanne Goldluecke (University of Bonn); Sebastian Kranz (University of Bonn) 
Abstract:  In this paper, we study inﬁnitely repeated games with imperfect public monitoring and the possibility of monetary transfers. We develop an effcient algorithm to compute the set of pure strategy public perfect equilibrium payoffs for each discount factor. We also show how all equilibrium payoffs can be implemented with a simple class of stationary equilibria that use stickandcarrot punishments. 
Date:  2010–07 
URL:  http://d.repec.org/n?u=RePEc:trf:wpaper:332&r=gth 
By:  Cédric Wasser (Humboldt University of Berlin) 
Abstract:  We consider a general class of imperfectly discriminating contests with privately informed players. We show that findings by Athey (2001) imply the existence of a Bayesian Nash equilibrium in monotone pure strategies. 
Keywords:  contest, imperfectly discriminating, asymmetric information, equilibrium existence, interdependent values 
JEL:  D72 D74 D82 C72 
Date:  2010–07 
URL:  http://d.repec.org/n?u=RePEc:trf:wpaper:331&r=gth 
By:  C. D. Aliprantis; I. Topolyan 
Abstract:  We propose an equilibrium refinement of strict perfect equilibrium for the finite normal form games, which is not known in the literature. Okada came up with the idea of strict perfect equilibrium by strengthening the main definition of a perfect equilibrium, due to Selten [14]. We consider the alternative (and equivalent) definition of perfect equilibrium, based on the substitute sequences, as appeared in Selten [14]. We show that by strengthening and modifiyng this definition slightly, one can obtain a refinement stronger than strict perfectness. We call the new refinement strict substitute perfect equilibrium. The main advantage of this solution concept is that it reflects the local dominance of an equilibrium point. An example is provided to show that a strict perfect equilibrium may fail to be strict substitute perfect. 
Keywords:  Perfect equilibrium, strictly perfect equilibrium, substitute sequence, substitute perfect equilibrium, unit simplex 
JEL:  C7 
Date:  2009–08 
URL:  http://d.repec.org/n?u=RePEc:pur:prukra:1225&r=gth 
By:  Michel Grabisch (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I); Agnieszka Rusinowska (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I) 
Abstract:  In the paper, we study a model of influence in a social network. It is assumed that each player has an inclination to say YES or NO which, due to influence of other players, may be different from the decision of the player. The point of departure here is the concept of the HoedeBakker index  the notion which computes the overall decisional `power' of a player in a social network. The main drawback of the HoedeBakker index is that it hides the actual role of the influence function, analyzing only the final decision in terms of success and failure. In this paper, we separate the influence part from the group decision part, and focus on the description and analysis of the influence part. We propose among other descriptive tools a definition of a (weighted) influence index of a coalition upon an individual. Moreover, we consider different influence functions representative of commonly encountered situations. Finally, we propose a suitable definition of a modified decisional power. 
Keywords:  influence function, influence index, decisional power, social network 
Date:  2010–07 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs00308741_v2&r=gth 
By:  Massimo Morelli; Dominic Rohner 
Abstract:  We examine how natural resource location, rent sharing and fighting capacities of different groups matter for ethnic conflict. A new type of bargaining failure due to multiple types of potential conflicts (and hence multiple threat points) is identified. The theory predicts conflict to be more likely when the geographical distribution of natural resources is uneven and when a minority group has better chances to win a secessionist rather than a centrist conflict. For sharing rents, resource proportionality is salient in avoiding secessions and strength proportionality in avoiding centrist civil wars. We present empirical evidence that is consistent with the model. 
Keywords:  Natural resources, conflict, strength proportionality, resource proportionality, secession, bargaining failure. 
JEL:  C72 D74 Q34 
Date:  2010–08 
URL:  http://d.repec.org/n?u=RePEc:zur:iewwpx:498&r=gth 
By:  Smeers, Y.; Oggioni, G.; Allevi, E.; Schaible, S. 
Abstract:  "Market Coupling'' is currently seen as the most advanced market design in the restructuring of the European electricity market. Market coupling, by construction, introduces what is generally referred to as an incomplete market: it leaves several constraints out of the market and hence avoids pricing them. This may or may not have important consequences in practice depending on the case on hand. QuasiVariational Inequality problems and the associated Generalized Nash Equilibrium can be used for representing incomplete markets. Recent papers propose methods for finding a set of solutions of QuasiVariational Inequality problems. We apply one of these methods to a subproblem of market coupling namely the coordination of countertrading. This problem is an illustration of a more general question encountered for instance in hierarchical planning in production management. We first discuss the economic interpretation of the QuasiVariational Inequality problem. We then apply the algorithmic approach to a set of stylized case studies in order to illustrate the impact of different organizations of countertrading. The paper emphazises the structuring of the problem. A companion paper considers the full problem of market coupling and countertrading and presents a more extensive numerical analysis. 
Keywords:  Generalized Nash Equilibrium, QuasiVariational Inequalities, Market Coupling, CounterTrading, European Electricity Market 
JEL:  D52 D58 Q40 
Date:  2010–08–16 
URL:  http://d.repec.org/n?u=RePEc:cam:camdae:1034&r=gth 
By:  Muthoo, Abhinay (Department of Economics, University of Warwick); Mutuswami, Suresh (Department of Economics, University of leicester) 
Abstract:  This paper studies the impact of competition on the degree of inefficiency in lemons markets. More precisely, we characterize the secondbest mechanism (i.e., the optimal mechanism with private information) in a stylized lemons market with finite numbers of buyers and sellers. We then study the relationship between the degree of efficiency of the secondbest mechanism and market competitiveness. The relationship between the firstbest and secondbest mechanisms is also explored. JEL Classification: C7 ; D4 ; D61 ; D82 
Date:  2010 
URL:  http://d.repec.org/n?u=RePEc:wrk:warwec:939&r=gth 