
on Game Theory 
By:  GRIGIS DE STEFANO, Federico (Université catholique de Louvain, CORE, Belgium) 
Abstract:  This paper introduces two set valued Nash equilibrium refinements that are a natural generalization of the concept of stable set of equilibria introduced in Kohlberg and Mertens (1986) and satisfy all the properties defined in Mertens (1989). It also establishes a connection between Nash equilibrium refinements and stochastic games as a tool to define a stable set of equilibria. 
Keywords:  game theory, equilibrium refinements, strategic stability, stochastic games 
JEL:  A23 C72 
Date:  2014–06–11 
URL:  http://d.repec.org/n?u=RePEc:cor:louvco:2014015&r=gth 
By:  Koshevoy, G.A.; Suzuki, T. (Tilburg University, Center For Economic Research); Talman, A.J.J. (Tilburg University, Center For Economic Research) 
Abstract:  A cooperative game with nontransferable utility (NTUgame) consists of a collection of payoffsets for the subsets of a nite set of players, for which it has to be determined how much payof each player must receive. The core of an NTUgame consists of all payoffvectors that are in the payoff set of the coalition of all players and cannot be improved upon by any coalition of players. For cooperative games with transferable utility (TUgames) the notion of convexity was introduced to guarantee that the Shapley value, being the average of all marginal vectors of the game, is an element of the core. Convexity of a TUgame is equivalent to supermodularity of the characteristic function underlying the game. In this paper we introduce the concept of supermodularity for NTUgames. Supermodularity for NTUgames is weaker than other existing types of convexity. Under supermodularity of an NTUgame it is shown that all appropriately dened marginal vectors of the game are elements of the core. As solution concept for NTUgames we propose a set of solutions that is determined by the average of all marginal vectors of the game. For TUgames the solution set coincides with the Shapley value of the game. Also conditions are stated under which the solution set is a subset of the core and is the set of bargaining solutions of a corresponding bargaining problem. 
Keywords:  core; shapley value; convexity; supermodularity; marginal vector 
JEL:  C71 
Date:  2014 
URL:  http://d.repec.org/n?u=RePEc:tiu:tiucen:23321d395b974a09b12060626df51653&r=gth 
By:  Selçuk, O. (Tilburg University, School of Economics and Management) 
Abstract:  Cooperative games with transferable utilities, or simply TUgames, refer to the situations where the revenues created by a coalition of players through cooperation can be freely distributed to the members of the coalition. The fundamental question in cooperative game theory deals with the problem of how much payoff every player should receive. The classical assumption for TUgames states that every coalition is able to form and earn the worth created by cooperation. In the literature, there are several different modifications of TUgames in order to cover the cases where cooperation among the players is restricted. The second chapter of this monograph provides a characterization of the average tree solution for TUgames where the restricted cooperation is represented by a connected cyclefree graph on the set of players. The third chapter considers TUgames for which the restricted cooperation is represented by a directed graph on the set of players and introduces the average covering tree solution and the dominance value for this class of games. Chapter four considers TUgames with restricted cooperation which is represented by a set system on the set of players and introduces the average coalitional tree solution for such structures. The last two chapters of this monograph belong to the social choice theory literature. Given a set of candidates and a set of an odd number of individuals with preferences on these candidates, pairwise majority comparison of the candidates yields a tournament on the set of candidates. Tournaments are special types of directed graphs which contain an arc between any pair of nodes. The Copeland solution of a tournament is the set of candidates that beat the maximum number of candidates. In chapter five, a new characterization of the Copeland solution is provided that is based on the number of steps in which candidates beat each other. Chapter six of this monograph is on preference aggregation which deals with collective decision making to obtain a social preference. A sophisticated social welfare function is defined as a mapping from profiles of individual preferences into a sophisticated social preference which is a pairwise weighted comparison of alternatives. This chapter provides a characterization of Pareto optimal and pairwise independent sophisticated social welfare functions. 
Date:  2014 
URL:  http://d.repec.org/n?u=RePEc:tiu:tiutis:0da8d0d308c24f8692a1335fbd2e64f3&r=gth 
By:  Jens Gudmundsson 
Abstract:  We study twosided ("marriage") and general pairing ("roommate") problems. We introduce "sequences," lists of matchings that are repeated in order. Stable sequences are natural extensions of stable matchings; case in point, we show that a sequence of stable matchings is stable. In addition, stable sequences can provide solutions to problems for which stable matchings do not exist. In a sense, they allow us to "balance" the interest of the agents at different matchings. In this way, sequences can be superior to matchings in terms of welfare and fairness. A seminal result due to Roth (1982, Math Oper Res 7(4), 617â628) is that no strategyproof rule always selects stable matchings. In contrast, we show that there is a weakly group sdstrategyproof rule that selects stable sequences. We call it the Compromises and Rewards rule, CR. We find that stronger incentive properties are incompatible with much weaker stability properties and vice versa. The CR rule satisfies two fairness axioms: anonymity and sideneutrality. For the general problem, the Generalized CR rule is sd5stable (cannot be blocked by groups of five or fewer agents), weakly sdstrategyproof, and anonymous. In addition, the Extended AllProposing Deferred Acceptance rule is sdstable, anonymous, and individually rational at all times on a restricted domain. We provide a condition under which our results still hold if agents have cardinal preferences and compare sequences using "expected utility." 
JEL:  C62 D02 D60 
Date:  2014–11–22 
URL:  http://d.repec.org/n?u=RePEc:jmp:jm2014:pgu351&r=gth 
By:  Luciana Cecilia Moscoso Boedo (Division of Economics, CIDE); Lucia Quesada; Marcela Tarazona 
Abstract:  Does the rotten apple spoils his companions? This is the question we analyze in the context of a repeated population game with behavioral types. Our experimental results show that the inclusion of a noncooperative player in an anonymous community makes cooperation much more difficult to sustain but that individuals still manage to trust some of the permanent players of society. The rotten apple lowers the quality of the companions, but is not able to completely spoil them. 
Keywords:  Population games, anonymous random matching, social norms. 
JEL:  C71 C93 
Date:  2013–11 
URL:  http://d.repec.org/n?u=RePEc:emc:wpaper:dte567&r=gth 
By:  Grundel, S. (Tilburg University, Center For Economic Research); Borm, P.E.M. (Tilburg University, Center For Economic Research); Hamers, H.J.M. (Tilburg University, Center For Economic Research) 
Abstract:  Abstract: In a resource allocation problem there is a commonpool resource, which has to be divided among agents. Each agent is characterized by a claim on this pool and an individual concave reward function on assigned resources. An assignment of resources is optimal if the total joint reward is maximized. We provide a necessary and sufficient condition for optimality of an assignment. Analyzing the associated allocation problem of the maximal total joint reward, we consider corresponding resource allocation games. It is shown that these games have a nonempty core and thus allow for stable allocations. Moreover, an explicit expression for the nucleolus of these games is provided. 
Keywords:  Resource Allocation Games; Concave Reward Function; Core; Nucleolus 
JEL:  C71 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:tiu:tiucen:b72ed3dcecc849d486afd4598cb9ddfd&r=gth 
By:  László Á. Kóczy (Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences and Keleti Faculty of Economics, Óbuda University) 
Abstract:  Power indices have been used to evaluate the allocation of power in a wide range of voting situations. While they use the language of game theory known measures of a priori voting power are hardly more than statistical expectations assuming the random behaviour of the players. We introduce a model where players can reject certain partnerships in cooperation. For normalised indices strategic rejection may increase power. Our notion of a strategic power index is well defined if power is measured by an index that takes only minimal winning coalitions into account. 
Keywords:  quarrelling, rejected coalitions, a priori voting power, power indices, minimal winning coalitions, rational players 
JEL:  C71 D71 
Date:  2014–11 
URL:  http://d.repec.org/n?u=RePEc:has:discpr:1431&r=gth 
By:  Luke Boosey (Department of Economics, Florida State University); R. Mark Isaac (Department of Economics, Florida State University) 
Abstract:  We report experimental findings on the impact of network structure on decentralized monitoring and punishment in public goods games. In the environment we study, individuals can only directly monitor and punish their immediate neighbors in an exogenously determined network. We examine contributions and punishment decisions in a Complete network, a Circle network, and an Asymmetric network. Average contributions are lower in the Asymmetric network, although this result is driven entirely by the player who faces only one potential punisher. We also examine whether asymmetry in the network leads some punishers to discriminate between their potential targets. After controlling for targets' contribution decisions, we find limited support for this hypothesis. However, the data indicate that some punishers may be deterred from issuing discriminatory punishment by undermonitored targets who retaliate against previous punishment more often than others. Thus, we identify an additional complication of asymmetry in the network  that it may facilitate more targeted revenge by undermonitored players. 
Keywords:  networks, public goods, punishment, revenge 
JEL:  C72 C91 C92 H41 
Date:  2014–12 
URL:  http://d.repec.org/n?u=RePEc:fsu:wpaper:wp2014_12_01&r=gth 
By:  Kleppe, J. (Tilburg University, Center For Economic Research); Reijnierse, J.H. (Tilburg University, Center For Economic Research); Sudhölter, P. 
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 Sobolev’s axiomatization of the prenucleolus and its modification for the nucleolus as well as Peleg’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 · Nucleolus · Kernel 
JEL:  C71 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:tiu:tiucen:98930f2c667e4a4ab76e85dd1d783896&r=gth 
By:  Florian Gauer (Center for Mathematical Economics, Bielefeld University) 
JEL:  D85 J64 Z13 
Date:  2014–11 
URL:  http://d.repec.org/n?u=RePEc:bie:wpaper:529&r=gth 
By:  Aniol LlorenteSaguer (Queen Mary University of London); Ro’i Zultan (BenGurion University) 
Abstract:  The theoretical literature on collusion in auctions suggests that the firstprice mechanism can deter the formation of bidding rings. In equilibrium, collusive negotiations are either successful or are avoided altogether, hence such analysis neglects the effects of failed collusion attempts. In such contingencies, information revealed in the negotiation process is likely to affect the bidding behavior in firstprice (but not secondprice) auctions. We test experimentally a setup in which collusion is possible, but negotiations often break down and information is revealed in an asymmetric way. The existing theoretical analysis of our setup predicts that the firstprice mechanism deters collusion. In contrast, we find the same level of collusion in firstprice and secondprice auctions. Furthermore, failed collusion attempts distort the bidding behavior in the ensuing auction, leading to loss of efficiency and eliminating the revenue dominance typically observed in firstprice auctions. 
Keywords:  Auctions, Collusion, Bribes, Experiment 
JEL:  C72 C91 D44 
Date:  2014–12 
URL:  http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp734&r=gth 
By:  Sagi Dekel (BGU); Sven Fischer (Max Planck Institute of Economics, Germany); Ro’i Zultan (BGU) 
Keywords:  public goods, punishment, reward, externalities. 
JEL:  C72 C91 H41 
Date:  2014 
URL:  http://d.repec.org/n?u=RePEc:bgu:wpaper:1405&r=gth 
By:  Hande Erkut (Department of Economics, Maastricht University); Daniele Nosenzo (University of Nottingham, School of Economics); Martin Sefton (University of Nottingham, School of Economics) 
Abstract:  We investigate social norms for dictator game giving using a recently proposed normelicitation procedure (Krupka and Weber, 2013). We elicit norms separately from dictator, recipient, and disinterested third party respondents and find that elicited norms are stable and insensitive to the role of the respondent. The results support the use of this procedure as a method for measuring social norms. 
Keywords:  social norms; dictator games 
URL:  http://d.repec.org/n?u=RePEc:not:notcdx:201416&r=gth 
By:  Krumer, Alex; Megidish, Reut; Sela, Aner 
Abstract:  We study roundrobin and elimination tournaments with three players where one player is dominant, i.e., he has a higher value of winning than his weaker opponents. In every stage, a pairwise match is modelled as an allpay auction. We demonstrate that the expected payoff of the weak players in the roundrobin tournament is higher than or equal to their expected payoffs in the elimination tournament. On the other hand, the expected payoff of the dominant player in the elimination tournament could be either higher or lower than in the roundrobin tournament. We also show that if a contest designer wishes to maximize the dominant player's probability to win he should organize a roundrobin tournament. However, if he wishes to maximize the players' expected total effort, then if the asymmetry between the players is relatively low, he should prefer the elimination tournament, while if the asymmetry is relatively high, he should prefer the roundrobin tournament. 
Keywords:  allpay auctions; elimination tournaments; roundrobin tournaments 
JEL:  D44 
Date:  2014–07 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:10081&r=gth 
By:  Huijink, S. (Tilburg University, Center For Economic Research); Borm, P.E.M. (Tilburg University, Center For Economic Research); Reijnierse, J.H. (Tilburg University, Center For Economic Research); Kleppe, J. (Tilburg University, Center For Economic Research) 
Abstract:  Abstract: This article characterizes the per capita nucleolus for bankruptcy games as a bankruptcy rule. This rule, called the cligths rule, is based on the wellknown constrained equal awards principle. The essential feature of the rule however is that, for each bankruptcy problem, it takes into account a vector of clights. These clights only depend on the vector of claims while the height of the estate determines whether the clights should be interpreted as modified claims or as rights. Finally, it is seen that both the clights rule and the AumannMaschler rule can be captured within the family of socalled claim and right rules. 
Keywords:  Bankruptcy; (per capita) nucleolus 
JEL:  C71 G33 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:tiu:tiucen:0b1d187ba25147c092d8722bc8c099df&r=gth 
By:  Benndorf, Volker; Kübler, Dorothea; Normann, HansTheo 
Abstract:  We study the voluntary revelation of private information in a labormarket experiment where workers can reveal their productivity at a cost. While rational revelation improves a worker's payoff, it imposes a negative externality on others and may trigger further revelation. Such unraveling can be observed frequently in our data although less often than predicted. Equilibrium play is more likely when subjects are predicted to conceal their productivity than when they should reveal. This tendency of underrevelation, especially of lowproductivity workers, is consistent with the levelk model. A loaded frame where the private information concerns the workers' health status leads to less revelation than a neutral frame. 
Keywords:  information revelation,levelk reasoning,privacy 
JEL:  C72 C90 C91 
Date:  2014 
URL:  http://d.repec.org/n?u=RePEc:zbw:dicedp:168&r=gth 
By:  Aguirregabiria, Victor; Vicentini, Gustavo 
Abstract:  We propose a dynamic model of an oligopoly industry characterized by spatial competition between multistore retailers. Firms compete in prices and decide where to open or close stores depending on demand conditions and the number of competitors at different locations, and on locationspecific privateinformation shocks. We develop an algorithm to approximate a Markov Perfect Equilibrium in our model, and propose a procedure for the estimation of the parameters of the model using panel data on number of stores, prices, and quantities at multiple geographic locations within a city. We also present numerical examples to illustrate the model and algorithm. 
Keywords:  cannibalization; industry dynamics; spatial competition; spatial preemption; store location; sunk costs 
JEL:  C73 L13 L81 R10 R30 
Date:  2014–11 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:10273&r=gth 