
on Game Theory 
Issue of 2013‒12‒20
ten papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University 
By:  Pablo Arribillaga; Jordi Massó; Alejandro Neme 
Abstract:  We study cooperative and competitive solutions for a many tomany generalization of Shapley and Shubik (1972)�s assignment game. We consider the Core, three other notions of group stability and two alternative definitions of competitive equilibrium. We show that (i) each group stable set is closely related with the Core of certain games defined using a proper notion of blocking and (ii) each group stable set contains the set of payoff vectors associated to the two definitions of competitive equilibrium. We also show that all six solutions maintain a strictly nested structure. Moreover, each solution can be identified with a set of matrices of (discriminated) prices which indicate how gains from trade are distributed among buyers and sellers. In all cases such matrices arise as solutions of a system of linear inequalities. Hence, all six solutions have the same properties from a structural and computational point of view. 
Keywords:  assignment game, competitive equilibrium, core, group stability 
JEL:  C78 D78 
Date:  2013–10 
URL:  http://d.repec.org/n?u=RePEc:bge:wpaper:740&r=gth 
By:  Ruijgrok, Matthijs; Ruijgrok, Theo 
Abstract:  The replicator equation for a two person symmetric game, which has an interval of the real line as strategy space, is extended with a mutation term. Assuming that the distribution of the strategies has a continuous density, a partial differential equation for this density is derived. The equation is analysed for two examples. A connection is made with Adaptive Dynamics. 
Keywords:  Evolutionary games; Replicator equation; Mutation; Dynamic stability; Partial differential equations 
JEL:  C72 C73 
Date:  2013–12–13 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:52198&r=gth 
By:  Gustavo Bergantiños; Jordi Massó; Inés Moreno de Barreda; Alejandro Neme 
Abstract:  We study how to partition a set of agents in a stable way when each coalition in the partition has to share a unit of a perfectly divisible good, and each agent has symmetric singlepeaked preferences on the unit interval of his potential shares. A rule on the set of preference profiles consists of a partition function and a solution. Given a preference profile, a partition is selected and as many units of the good as the number of coalitions in the partition are allocated, where each unit is shared among all agents belonging to the same coalition according to the solution. A rule is stable at a preference profile if no agent strictly prefers to leave his coalition to join another coalition and all members of the receiving coalition want to admit him. We show that the proportional solution and all sequential dictator solutions admit stable partition functions. We also show that stability is a strong requirement that becomes easily incompatible with other desirable properties like efficiency, strategyproofness, anonymity, and nonenvyness. 
Keywords:  division problem, symmetric singlepeaked preferences, stable partition 
JEL:  D71 
Date:  2013–10 
URL:  http://d.repec.org/n?u=RePEc:bge:wpaper:739&r=gth 
By:  Aviad Heifetz; Willemien Kets 
Abstract:  In an important paper, Weinstein and Yildiz (2007) show that if players have an innite depth of reasoning and this is commonly believed, types generically have a unique rationalizable action in games that satisfy a richness condition. We show that this result does not extend to environments where players may have a finite depth of reasoning, or think it is possible that the other player has a finite depth of reasoning, or think that the other player may think that is possible, and so on, even if this socalled "grain of naivete" is arbitrarily small. More precisely, we show that even if there is almost common belief in the event that players have an infinite depth of reasoning, there are types with multiple rationalizable actions, and the same is true for "nearby" types. Our results demonstrate that both uniqueness and multiplicity are robust phenomena when we relax the assumption that it is common belief that players have an infinite depth, if only slightly. 
Keywords:  Bounded rationality, finite depth of reasoning, global games, higherorder beliefs, generic uniqueness, robust multiplicity JEL Classification: C700, C720, D800, D830 
Date:  2013–12–11 
URL:  http://d.repec.org/n?u=RePEc:nwu:cmsems:1573&r=gth 
By:  Gustavo Bergantiños; Jordi Massó; Alejandro Neme 
Abstract:  The division problem under constraints consists of allocating a given amount of an homogeneous and perfectly divisible good among a subset of agents with single peaked preferences on an exogenously given interval of feasible allotments. We char acterize axiomatically the family of extended uniform rules proposed to solve the division problem under constraints. Rules in this family extend the uniform rule used to solve the classical division problem without constraints. We show that the fam ily of all extended uniform rules coincides with the set of rules satisfying efficiency, strategyproofness, equal treatment of equals, bound monotonicity, consistency, and independence of irrelevant coalitions. 
Keywords:  Division Problem, Singlepeaked Preferences. 
JEL:  D71 
Date:  2013–12–16 
URL:  http://d.repec.org/n?u=RePEc:aub:autbar:942.13&r=gth 
By:  Heuson, Clemens 
Abstract:  This paper analyses the outcome of noncooperative national efforts in combatting global pollution problems when governments are elected by their citizens. It is wellknown that the latter tend to vote governments that are less 'green' than the median voter in order to commit to lower national mitigation efforts, which further increases the inefficiently high amount of global emissions. However, the present paper shows that the option of selfprotection against environmental damages, which has been invariably neglected in the relevant literature to date, alleviates or even completely offsets such strategic delegation and the related adverse effects.  
Keywords:  strategic delegation,global pollution problems,selfprotection,noncooperative behaviour 
JEL:  C72 D72 H41 Q58 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:zbw:ufzdps:182013&r=gth 
By:  D. Dragone; F. Galeotti; R. Orsini 
Abstract:  We conduct an artefactual field experiment to study whether the individual preferences and propensity to cooperate of temporary workers differ from permanent contract workers. We find that temporary and permanent contract workers have different otherregarding preferences, but display similar contribution patterns in an anonymous Public Good Game. Students, instead, are more selfish and contribute less than temporary and permanent workers. 
JEL:  C72 C93 D23 H41 J54 
Date:  2013–12 
URL:  http://d.repec.org/n?u=RePEc:bol:bodewp:wp915&r=gth 
By:  Masili, Gustavo 
Abstract:  For any political party wishing to keep the governance of the country, it is crucial to understand the power that each of the other parties can bring to its coalition. This evaluation helps to understand the bargaining power of each party individually. Furthermore, it allows a party to evaluate alternative alliances that may require less counterparts and that offers more power. This paper presents the historical evolution of the theory of voting power and an analysis of the voting power of each of the Brazilian parties, as well as some strategic alliances, for both the Chamber of Deputies and the Senate. 
Keywords:  Voting Power, Political Parties, Alliances; Legislative Behavior. 
JEL:  C72 D72 D74 
Date:  2013–12 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:52170&r=gth 
By:  Wolf, Stephan; Lenger, Alexander 
Abstract:  Mainstream economists usually identify a fundamental conflict between efficiency and justice in resource allocation: markets are generally considered an efficient allocation tool, but create unequal results. Corresponding governmental redistribution shall equalize some of these market results, but leads to inefficiency due to disincentives both for net payers and net receivers. Consequently, this paper analyses the impact of social inequality on distributive choices in an experimental democracy. In our experiment, we find that stark inequality is generally accepted provided a strong egalitarian income floor is ensured. Even though our samples showed a very strong egalitarian inclination, complete egalitarianism was not a stable outcome. Some degree of differentiation always emerged on an initial egalitarian base.  
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:zbw:cenwps:022013&r=gth 
By:  Nedelchev, Miroslav 
Abstract:  What happenned after 2007 requires that new kind of instruments are applied in order to face the global financial crisis. Noncoordinated actions undertaken by a single bank group have additionally sharpened the effects of the crisis and have resulted in the must of joint efforts which are better known as the "prisoner's dilema". 
Keywords:  prisoner’s dilemma, bank groups, corporate governance 
JEL:  C71 G21 G34 
Date:  2012–09 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:52247&r=gth 