
on Game Theory 
By:  Pierre Bernhard (Université Côte d’Azur, INRIA); Marc Deschamps (Université de Bourgogne FrancheComté, CRESE) 
Abstract:  There are real strategic situations where nobody knows ex ante how many players there will be in the game at each step. Assuming that entry and exit could be modelized by random processes whose probability laws are common knowledge, we use dynamic programming and piecewise deterministic Markov decision processes to investigate such games. We study the dynamic equilibrium in games with randomly arriving players in discrete and continuous time for both finite and infinite horizon. Existence of dynamic equilibrium in discrete time is proved and we develop explicit algorithms for both discrete and continuous time linear quadratic problems. In both cases we offer a resolution for a Cournot oligopoly with sticky prices. 
Keywords:  Nash equilibrium, Dynamic programming, Piecewise Deterministic Markov Decision Process, Cournot oligopoly, Sticky Prices. 
JEL:  C72 C61 L13 
Date:  2016–10 
URL:  http://d.repec.org/n?u=RePEc:crb:wpaper:201610&r=gth 
By:  Calford, Evan 
Abstract:  In normal form games, when agents exhibit ambiguity aversion the exclusion of mixed strategies from agents' choice sets can enlarge the set of equilibria. While it is possible, in a game theoretic experiment, to enforce pure strategy reporting it is not possible to prevent subjects from mixing before reporting a pure strategy. This short paper establishes conditions under which the set of equilibrium in a game with ambiguity averse agents and pure strategy reporting is invariant to the existence of preplay mixing devices. This result is crucial for the interpretation of recent experimental work on the role of ambiguity aversion in normal form games. 
Keywords:  Ambiguity Aversion, Mixed Strategies, Game Theory, Experimental Economics 
JEL:  C72 C92 D03 D81 
Date:  2016–10–31 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:74909&r=gth 
By:  Ning Sun; Zaifu Yang 
Abstract:  Abstract: We study a general model of marriage in which there are finitely many singles (unmarried men or women) and married couples. Singles wish to marry. Married couples can divorce and thus remarry as long as both parties will not be made worse off than they maintain the status quo. This is called mutual consent divorce. We examine the problem of how to make marriages between men and women as well as possible by allowing mutual consent divorce. We show the existence of a nonempty core of marriage matchings and also propose a finite procedure for finding a core matching. The procedure is a novel blend of modifications of two celebrated algorithms: the deferred acceptance procedure of Gale and Shapley (1962) and the top trading cycle method from Shapley and Scarf (1974). 
Keywords:  Marriage, core, stability, mutual consent divorce, partial commitment. 
JEL:  C71 C78 J12 
Date:  2016–11 
URL:  http://d.repec.org/n?u=RePEc:yor:yorken:16/14&r=gth 
By:  Suvi Vasama; ; 
Abstract:  We examine collaboration in a onearm bandit problem in which the players' actions affect the distribution over future payoffs. The players need to exert costly effort both to enhance the value of a risky technology and to learn about its current state. Both product value and learning are public goods, which gives the players incentives to freeride on each others' actions. This leads to an inefficiently low aggregate level of effort. When the players' actions affect the distribution over future payoffs, they eventually get trapped in the low action, causing an inefficient unraveling of the game. Moreover, the players' incentives to exert effort depend on the state that in turn depends on the aggregate effort. If the players start restricting effort when the belief decreases in expectation, the two effects play in the same direction. Higher effort encourages higher effort and vice versa. Unraveling leads to multiple symmetric Markov perfect equilibria. 
JEL:  C73 D83 O31 
Date:  2016–10 
URL:  http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2016048&r=gth 
By:  Bergantiños, Gustavo; VidalPuga, Juan 
Abstract:  We study hub problems where a set of nodes send and receive data from each other. In order to reduce costs, the nodes use a network with a given set of hubs. We address the cost sharing aspect by assuming that nodes are only interested in either sending or receiving data, but not both (oneway flow) or that nodes are interested in both sending and receiving data (twoway flow). In both cases, we study the nonemptiness of the core and the Shapley value of the corresponding cost game. 
Keywords:  hub network; cost allocation; core; Shapley value 
JEL:  C71 
Date:  2016–11–02 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:74875&r=gth 
By:  Ambec, Stefan; Garapin, Alexis; Muller, Laurent; Rahali, Bilel 
Abstract:  We investigate how people trade off between equity and efficiency, using variations of tripled dictator and trust games in a lab experiment. Equalizing payoffs reduces the return from the tripled investment in the dictator game. In contrast, in the trust game both equal and maximized payoffs can be achieved, provided that receiver transfers back half of the return from investment. We find that subjects sacrifice efficiency for equity in the dictator game but manage to achieve both in the trust game. Most subjects equalize payoffs when they are placed behind a veil of ignorance about their position in the trust game, regardless of their aversion to risk. They invest less when they pay to obtain their position as investor but do not send back less if they pay to be the receiver. Subjects who modify their investment decision after receiving information about the average investment in their group tend to move closer to the average. 
Keywords:  Trust game, triple dictator game, fairness, efficiency, equity, experiment. 
JEL:  C72 C90 D03 D63 
Date:  2016–10 
URL:  http://d.repec.org/n?u=RePEc:tse:wpaper:31118&r=gth 
By:  Lazarova, E.A. (Tilburg University, School of Economics and Management); Borm, Peter (Tilburg University, School of Economics and Management); Estevez, Arantza 
Abstract:  In this paper we consider onetomany matching problems where the preferences of the agents involved are represented by monetary reward functions. We characterize Pareto optimal matchings by means of contractual exchange stability and matchings of maximum total reward by means of compensational exchange stability. To conclude, we show that in going from an initial matching to a matching of maximum total reward, one can always provide a compensation schedule that will be expost stable in the sense that there will be no subset of agents who can all by deviation obtain a higher reward. The proof of this result uses the fact that the core of an associated compensation matching game with constraints is nonempty. 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:tiu:tiutis:e76da65ec6924ba3a2c6dd9264acdb1b&r=gth 
By:  Zhenhua Pei; Baokui Wang; Jinming Du 
Abstract:  Income redistribution is the transfer of income from some individuals to others directly or indirectly by means of social mechanisms, such as taxation, public services and so on. Employing a spatial public goods game, we study the influence of income redistribution on the evolution of cooperation. Two kinds of evolutionary models are constructed, which describe local and global redistribution of income respectively. In the local model, players have to pay part of their income after each PGG and the accumulated income is redistributed to the members. While in the global model, all the players pay part of their income after engaging in all the local PGGs, which are centered on himself and his nearest neighbours, and the accumulated income is redistributed to the whole population. We show that the cooperation prospers significantly with increasing income expenditure proportion in the local redistribution of income, while in the global model the situation is opposite. Furthermore, the cooperation drops dramatically from the maximum curvature point of income expenditure proportion. In particular, the intermediate critical points are closely related to the renormalized enhancement factors. 
Date:  2016–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1611.01531&r=gth 
By:  GiménezGómez, José M. (Universitat Rovira i Virgili, Departament d'Economia and CREIP); Peris, Josep E. (University of Alicante, D. Quantitative Methods and Economic Theory); Subiza, Begoña (University of Alicante, D. Quantitative Methods and Economic Theory) 
Abstract:  A minimum cost spanning tree problem analyzes the way to efficiently connect individuals to a source when they are located at different places. Several rules have been defined to solve this problem. Our objective here is to propose a new approach that differentiates some costs that may deserve compensations (involuntary costs) from some other connection costs that may be considered voluntary. We therefore define a solidarity egalitarian solution, through which, the total cost is allocated by considering paybacks to equalize the involuntary costs, thus fulfilling the weak stability condition of individual rationality. 
Keywords:  Minimum cost spanning tree; Solidarity; Cost sharing; Egalitarian 
JEL:  C71 D63 D71 
Date:  2016–11–07 
URL:  http://d.repec.org/n?u=RePEc:ris:qmetal:2016_005&r=gth 
By:  Sylvain Béal (Université de Bourgogne FrancheComté, CRESE); Sylvain Ferrières (Université de Bourgogne FrancheComté, CRESE); Eric Rémila (Université de SaintEtienne, Gate); Phillippe Solal (Université de SaintEtienne, Gate) 
Abstract:  A variant of the hindex introduced in GarciaPerez (2009), called the iterated hindex, is studied to evaluate the productivity of scholars. It consists of successive applications of the hindex so as to obtain a vector of hindices. In particular, the iterated hindex fixes a drawback of the hindex since it allows for (lexicographic) comparisons of scholars with the same hindex. Two types or results are presented. Firstly, we provide an axiomatic characterization of the iterated hindex, which rests on a new axiom of consistency and extensions of axioms in the literature to a richer framework. Secondly, we apply the hindex and iterated hindex to offer alternative sport rankings in tennis, football and basketball. These applications clearly demonstrate that the iterated hindex is much more appropriate than the classical hindex. 
Keywords:  hindex, iterated hindex, axioms, sports ranking 
JEL:  D70 Z20 
Date:  2016–10 
URL:  http://d.repec.org/n?u=RePEc:crb:wpaper:201611&r=gth 
By:  Karos, Dominik (General Economics 1 (Micro)); Peters, Hans (QE / Mathematical economics and game the) 
Abstract:  We axiomatically develop a class of power indices for effectivity functions, both for the case where the set of alternatives is finite and where it is infinite. Such power indices make it possible to take the issues under consideration into account, in contrast to power indices defined just for simple games. As an example, we consider the US legislative system. We also show that our approach can be used to develop power indices for spatial political games. 
Keywords:  Effectivity Function, Power Index 
JEL:  C71 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:unm:umagsb:2016034&r=gth 