
on Game Theory 
Issue of 2013‒03‒02
twelve papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University 
By:  Peter Duersch; Joerg Oechssler; Burkhard Schipper (Department of Economics, University of California Davis) 
Abstract:  We characterize the class of symmetric twoplayer games in which titfortat cannot be beaten even by very sophisticated opponents in a repeated game. It turns out to be the class of exact potential games. More generally, there is a class of simple imitation rules that includes titfortat but also imitatethebest and imitateifbetter. Every decision rule in this class is essentially unbeatable in exact potential games. Our results apply to many interesting games including all symmetric 2x2 games, and standard examples of Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games. 
Keywords:  Imitation, titfortat, decision rules, learning, exact potential games, symmetric games, repeated games, relative payoffs, zerosum games 
JEL:  C72 C73 D43 
Date:  2013–01–22 
URL:  http://d.repec.org/n?u=RePEc:cda:wpaper:131&r=gth 
By:  Andreas M. Hefti 
Abstract:  This paper investigates the relationship between uniqueness of Nash equilibria and local stability with respect to the bestresponse dynamics in the cases of sumaggregative and symmetric games. If strategies are equilibrium complements, local stability and uniqueness are the same formal properties of the game. With equilibrium substitutes, local stability is stronger than uniqueness. If players adjust sequentially rather than simultaneously, this tends towards making a symmetric equilibria of symmetric games more stable. Finally, the relationship between the stability of the Nash bestresponse dynamics is compared to the stability of the responsedynamics induced by aggregatetaking behavior. 
Keywords:  Contraction mapping, stability, uniqueness, aggregatetaking behavior, dominance solvability, symmetric games 
JEL:  C72 D43 L13 
Date:  2013–02 
URL:  http://d.repec.org/n?u=RePEc:zur:econwp:112&r=gth 
By:  Kleppe, J.; Reijnierse, J.H.; SudhÃ¶lter, P. (Tilburg University, Center for Economic Research) 
Abstract:  If the excesses of the coalitions in a transferable utility game are weighted, then we show that the arising weighted modifications of the wellknown (pre)nucleolus and (pre)kernel satisfy the equal treatment property if and only if the weight system is symmetric in the sense that the weight of a subcoalition of a grand coalition may only depend on the grand coalition and the size of the subcoalition. Hence, the symmetrically weighted versions of the (pre)nucleolus and the (pre)kernel are symmetric, i.e., invariant under symmetries of a game. They may, however, violate anonymity, i.e., they may depend on the names of the players. E.g., a symmetrically weighted nucleolus may assign the classical nucleolus to one game and the per capita nucleolus to another game. We generalize Sobolevâ€™s axiomatization of the prenucleolus and its modification for the nucleolus as well as Pelegâ€™s axiomatization of the prekernel to the symmetrically weighted versions. Only the reduced games have to be replaced by suitably modified reduced games whose definitions may depend on the weight system. Moreover, it is shown that a solution may only satisfy the mentioned sets of modified axioms if the weight system is symmetric. 
Keywords:  TU game Â· Nucleolus Â· Kernel 
JEL:  C71 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:dgr:kubcen:2013007&r=gth 
By:  Daniel Cardona (Universitat de les Illes Balears); Antoni RubíBarceló (Universitat de les Illes Balears) 
Abstract:  This note analyzes the efficiency properties of the equilibrium in a multilateral bargaining game in which a legislature divides a budget among collective and particularistic goods. We extend the model of Volden and Wiseman (2007) by considering smooth utility functions and consensus requirements ranging from simplemajority to unanimity. We show that when the private valuation of the private good is relatively high, only unanimity induces an (exante) Pareto efficient outcome. Moreover, optimality can be easily attained by using sequential negotiations, independently of the majority requirement. 
Keywords:  Noncooperative bargaining, sequential negotiantion, voting, quota rules 
JEL:  C72 C78 D72 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:ubi:deawps:53&r=gth 
By:  Mohamed Belhaj (Centrale Marseille, (AixMarseille School of Economics), CNRS and EHESS); Sebastian Bervoets (AixMarseille University (AixMarseille School of Economics), CNRS and EHESS); Frédéric Deroïan (AixMarseille University (AixMarseille School of Economics), CNRS and EHESS) 
Abstract:  We consider agents playing a linear network game with strategic complementarities. We analyse the problem of a policy maker who can change the structure of the network in order to increase the aggregate efforts of the individuals and/or the sum of their utilities, given that the number of links of the network has to remain fixed. We identify some link reallocations that guarantee an improvement of aggregate efforts and/or aggregate utilities. With this comparative statics exercise, we then prove that the networks maximising both aggregate outcomes (efforts and utilities) belong to the class of NestedSplit Graphs. 
Keywords:  Network, Linear Interaction, Bonacich Centralities, Strategic Complementarity, Nested Split Graphs. 
JEL:  C72 D85 
Date:  2013–02–12 
URL:  http://d.repec.org/n?u=RePEc:aim:wpaimx:1309&r=gth 
By:  Andersson , Tommy (Department of Economics, Lund University); Gudmundsson , Jens (Department of Economics, Lund University); Talman , Adolphus (CentER, Tilburg University); Yang , Zaifu (Department of Economics and Related Studies, University of York) 
Abstract:  A group of heterogeneous agents may form partnerships in pairs. All single agents as well as all partnerships generate values. If two agents choose to cooperate, they need to specify how to split their joint value among one another. In equilibrium, which may or may not exist, no agents have incentives to break up or form new partnerships. This paper proposes a dynamic competitive adjustment process that always either finds an equilibrium or exclusively disproves the existence of any equilibrium in finitely many steps. When an equilibrium exists, partnership and revenue distribution will be automatically and endogenously determined by the process. Moreover, several fundamental properties of the equilibrium solution and the model are derived. 
Keywords:  Partnership formation; adjustment process; equilibrium; assignment market 
JEL:  C62 C72 D02 
Date:  2013–02–04 
URL:  http://d.repec.org/n?u=RePEc:hhs:lunewp:2013_002&r=gth 
By:  Sebastian Kranz (Dept. of Mathematics and Economics, University of Ulm) 
Abstract:  We propose a unified framework to study relational contracting and holdup problems in infinite horizon stochastic games. We first illustrate that with respect to long run decisions, the common formulation of relational contracts as Paretooptimal public perfect equilibria is in stark contrast to fundamental assumptions of holdup models. We develop a model in which relational contracts are repeatedly newly negotiated during relationships. Negotiations take place with positive probability and cause bygones to be bygones. Traditional relational contracting and holdup formulations are nested as opposite corner cases. Allowing for intermediate cases yields very intuitive results and sheds light on many plausible tradeoffs that do not arise in these corner cases. We establish a general existence result and a tractable characterization for stochastic games in which money can be transferred. This paper formulates a theory of relational contracting in dynamic games. A crucial feature is that existing relational contracts can depreciate and ensuing negotiations then treat previous informal agreements as bygones. The model nests the traditional formulation of relational contracts as Paretooptimal equilibria as a special case. In repeated games both formulations are always mathematically equivalent. We provide ample illustrations that in dynamic games the traditional formulation is restrictive in so far that it rules out by assumption many plausible holdup problems  even for small discount factors. Our model provides a framework that naturally unifies the analysis of relational contracting and holdup problems. 
Keywords:  Relational contracting, Holdup, Negotiations, Stochastic games 
JEL:  C73 C78 D23 L14 
Date:  2013–02 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:1888&r=gth 
By:  Baron, David P. (Stanford University); Bowen, T. Renee (Stanford University) 
Abstract:  Policymaking is a dynamic process in which policies can be changed in each period but continue in the absence of new legislation. We study a dynamic legislative bargaining game with an endogenous status quo where in each period a dollar is allocated with a proposal voted against the allocation in the previous period. We characterize for any initial status quo a class of simple Markov perfect equilibria (MPE) with dynamic coalitions, where a dynamic coalition is a decisive set of legislators whose members support the same policy, or set of policies, in at least two consecutive periods. In the basic model a dynamic coalition persists throughout the game, and coalition members share the dollar equally in every period. If uncertainty is associated with the implementation of a policy, there is a continuum of allocations supported by coalition MPE in which the originator of the coalition receives a share larger than the coalition partner receives but smaller than in sequential legislative bargaining theory. These coalition equilibria have the same allocation in every period when the coalition persists, but with positive probability the coalition dissolves due to the uncertainty. Coalition MPE also exists in which members tolerate a degree of implementation uncertainty resulting in coalition allocations that can change from one period to the next. The dynamic coalitions are minimal winning, form in the first period, and, if a coalition dissolves, a new coalition is formed in the next period. The predictions of the theory are compared to experiment results. 
JEL:  C73 D72 
Date:  2013–01 
URL:  http://d.repec.org/n?u=RePEc:ecl:stabus:2128&r=gth 
By:  Bobtcheff, Catherine (Toulouse School of Economics (CNRS, LERNA)); Bolte, Jérôme (Toulouse School of Economics (GREMAQ)); Mariotti, Thomas (Toulouse School of Economics (CNRS, GREMAQ, IDEI)) 
Abstract:  We model academic competition as a game in which researchers ¯ght for priority. Researchers privately experience breakthroughs and decide how long to let their ideas mature before making them public, thereby establishing priority. In a tworesearcher, symmetric environment, the resulting preemption game has a unique equilibrium. We study how the shape of the breakthrough distribution affects equilibrium maturation delays. Making researchers better at discovering new ideas or at developing them has contrasted effects on the quality of research outputs. Finally, when researchers have different innovative abilities, speed of discovery and maturation of ideas are positively correlated in equilibrium. 
Keywords:  Academic Competition, Preemption Games, Private Information. 
JEL:  C73 D82 
Date:  2013–02 
URL:  http://d.repec.org/n?u=RePEc:tse:wpaper:26783&r=gth 
By:  Bigoni, Maria (University of Bologna); Casari, Marco (University of Bologna); Skrzypacz, Andrzej (Stanford University); Spagnolo, Giancarlo (SITE, Stockholm School of Economics and University of Rome "Tor Vergata") 
Abstract:  When subjects interact in continuous time, their ability to cooperate may dramatically increase. In an experiment, we study the impact of different time horizons on cooperation in (quasi) continuous time prisoner's dilemmas. We find that cooperation levels are similar or higher when the horizon is deterministic rather than stochastic. Moreover, a deterministic duration generates different aggregate patterns and individual strategies than a stochastic one. For instance, under a deterministic horizon subjects show high initial cooperation and a strong endofperiod reversal to defection. Moreover, they do not learn to apply backward induction but to postpone defection closer to the end. 
JEL:  C72 C73 C91 C92 D74 
Date:  2013–02 
URL:  http://d.repec.org/n?u=RePEc:ecl:stabus:2088r&r=gth 
By:  Ronald Stauber 
Abstract:  This paper defines simple procedures to construct ambiguous perturbations of belief structures associated to standard type spaces with precise beliefs, based on ambiguous type spaces whose induced belief hierarchies approximate the belief hierarchies corresponding to the initial type space. Two alternative procedures to construct such perturbations are introduced, and are shown to yield a simple and intuitive characterization of convergence of the resulting approximations to the initial unperturbed environment. The perturbations arising from one of these procedures include the set of all finite perturbations as a special case. The introduced perturbations and their convergence properties provide a foundation for the analysis of robustness to ambiguity of various solutions concepts, and for various decision rules under ambiguity. 
JEL:  C72 D83 
Date:  2013–02 
URL:  http://d.repec.org/n?u=RePEc:acb:cbeeco:2013602&r=gth 
By:  Antonio Cabrales; Piero Gottardo; Fernando VegaRedondo 
Abstract:  The aim of this paper is to investigate how the capacity of an economic system to absorb shocks depends on the specific pattern of interconnections established among financial firms. The key tradeoff at work is between the risksharing gains enjoyed by firms when they become more interconnected and the largescale costs resulting from an increased risk exposure. We focus on two dimensions of the network structure: the size of the (disjoint) components into which the network is divided, and the "relative density" of connections within each component. We find that when the distribution of the shocks displays "fat" tails extreme segmentation is optimal, while minimal segmentation and high density are optimal when the distribution exhibits "thin" tails. For other, less regular distributions intermediate degrees of segmentation and sparser connections are also optimal. We also find that there is typically a conflict between efficiency and pairwise stability, due to a "size externality" that is not internalized by firms who belong to components that have reached an individually optimal size. Finally, optimality requires perfect assortativity for firms in a component. 
Keywords:  Firm networks, Contagion, Risk Sharing 
JEL:  D85 C72 G21 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:eui:euiwps:eco2013/01&r=gth 