
on Game Theory 
Issue of 2011‒11‒21
fourteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University 
By:  Michel Grabisch (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris); Alexandre Skoda (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I) 
Abstract:  We study cooperative games associated with a communication structure which takes into account a level of communication between players. Let us consider an undirected communication graph : each node represents a player and there is an edge between two nodes if the corresponding players can communicate directly. Moreover we suppose that a weight is associated with each edge. We compute the socalled strength of this graph and use the corresponding partition to determine a particular coalition structure. The strength of a graph is a measure introduced in graph theory to evaluate the resistance of networks under attacks. It corresponds to the minimum on all subsets of edges of the ratio between the sum of the weights of the edges and the number of connected components created when the set of edges is suppressed from the graph. The set of edges corresponding to the minimum ratio induces a partition of the graph. We can iterate the calculation of the strength on the subgraphs of the partition to obtain refined partitions which we use to define a hierarchy of coalition structures. For a given game on the graph, we build new games induced by these coalition structures and study the inheritance of convexity properties, and the Shapley value associated with them. 
Keywords:  Communication networks, coalition structure, cooperative game. 
Date:  2011–07 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs00639685&r=gth 
By:  Nagore Iriberri (Universitat Pompeu Fabra); José Ramón Uriarte (UPV/EHU) 
Abstract:  We study a society inside which two official languages, the majority language A and the minority language B, are in contact and compete for the same social functions. We propose a noncooperative game to capture some features of this competitive situation. In the game, there are two types of players: the bilingual one who speaks both A and B and the monolingual one who speaks only A. The information about which type is each player is private. A real life situation captured by the game is that in many interactions bilingual players must decide under incomplete information about which language to use. One implication of this information structure is that while A satisfies the main properties of a public good, B does not. Another implication is that it may have dangerous consequences on the language diversity of the society. We show that in many equilibria bilingual players fail to coordinate in their preferred language and end up using the majority language A. 
Date:  2011–11–15 
URL:  http://d.repec.org/n?u=RePEc:ehu:ikerla:200624&r=gth 
By:  Koshevoy, G.A.; Talman, A.J.J. (Tilburg University, Center for Economic Research) 
Abstract:  We introduce a theory on marginal values and their core stability for cooperative games with arbitrary coalition structure. The theory is based on the notion of nested sets and the complex of nested sets associated to an arbitrary set system and the Mextension of a game for this set. For a set system being a building set or partition system, the corresponding complex is a polyhedral complex, and the vertices of this complex correspond to maximal strictly nested sets. To each maximal strictly nested set is associated a rooted tree. Given characteristic function, to every maximal strictly nested set a marginal value is associated to a corresponding rooted tree as in [9]. We show that the same marginal value is obtained by using the Mextension for every permutation that is associated to the rooted tree. The GCsolution is defined as the average of the marginal values over all maximal strictly nested sets. The solution can be viewed as the gravity center of the image of the vertices of the polyhedral complex. The GCsolution differs from the Myersonkind value defined in [2] for union stable structures. The HSsolution is defined as the average of marginal values over the subclass of socalled halfspace nested sets. The NTsolution is another solution and is defined as the average of marginal values over the subclass of NTnested sets. For graphical buildings the collection of NTnested sets corresponds to the set of spanning normal trees on the underlying graph and the NTsolution coincides with the average tree solution. We also study core stability of the solutions and show that both the HSsolution and NTsolution belong to the core under halfspace supermodularity, which is a weaker condition than convexity of the game. For an arbitrary set system we show that there exists a unique minimal building set containing the set system. As solutions we take the solutions for this building covering by extending in a natural way the characteristic function to it by using its MÃ¶bius inversion. 
Keywords:  Core;polytope;building set;nested set complex;MÃ¶bius inversion;permutations;normal fan;average tree solution;Myerson value. 
JEL:  C71 
Date:  2011 
URL:  http://d.repec.org/n?u=RePEc:dgr:kubcen:2011119&r=gth 
By:  Simone Galperti 
Abstract:  I analyze common agency games in which the principals, and possibly the agent,have private information. I distinguish between games in which the principals delegate the fi nal decisions to the agent, and games in which they retain some decision power after offering their mechanisms. I show that,in contrast with mechanism design models with one informed Myerrson's Inscrutability Principle fails when there are many informed principals. I also find that, in contrast with common agency models with uninformed principals, the Delegation Principle (Menu Theorem) fails when principals are informed. I then focus on Perfect Bayesian Equilibria in which principals offer their mechanisms without randomizing. I characterize the outcomes of arbitrary games with delegation as outcomes of a new game in which principals offer menus and send cheaptalk signals. Next, I characterize the outcomes of arbitrary games without delegation as outcomes of a new game in which principals offer menus of direct revelation mechanisms, to which they truthfully report their types. JEL Code: C18, C53, D89 
Keywords:  Common agency, informed principals, Inscrutability Principle, Delegation Principle, menus, signals, direct revelation mechanisms. 
Date:  2011–30–31 
URL:  http://d.repec.org/n?u=RePEc:nwu:cmsems:1541&r=gth 
By:  Rachmilevitch, Shiran (Department of Economics, University of Haifa) 
Abstract:  A bargaining solution guarantees minimal equity if each player's payoff is at least as large as the minimum of the payoffs assigned to him by the equalgain (i.e., egalitarian) and equalloss solutions. The KalaiSmorodinsky solution is the unique scaleinvariant 2person solution with this property. There does not exist a scaleinvariant nperson solution with this property. 
Keywords:  Bargaining; fairness; KalaiSmorodinsky solution 
JEL:  D63 D71 
Date:  2011–11–03 
URL:  http://d.repec.org/n?u=RePEc:haf:huedwp:wp201112&r=gth 
By:  Michel Grabisch (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris); Agnieszka Rusinowska (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I) 
Abstract:  The paper concerns a dynamic model of influence in which agents have to make a yesno decision. Each agent has an initial opinion, which he may change during different phases of interaction, due to mutual influence among agents. The influence mechanism is assumed to be stochastic and to follow a Markov chain. In the paper, we investigate a model of influence based on aggregation functions. Each agent modifies his opinion independently of the others, by aggregating the current opinion of all agents, possibly including himself. We provide a general analysis of convergence in the aggregation model and give more practical conditions based on influential players. We show that the process of influence converges always to one of the two consensus states, and there may exist other terminal classes, which are either cyclic or union of Boolean lattices. We give sufficient conditions for avoiding these additional terminal classes, based on properties of the graph of influence and influential players. We also introduce the notion of influential coalition and show that it can fully describe terminal classes. Some important families of aggregation functions are discussed. 
Keywords:  Influence, aggregation function, convergence, terminal class, influential coalition, social network. 
Date:  2011–10 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs00639677&r=gth 
By:  Heifetz, Aviad (Open University of Israel); Meier, Martin (Institute of Advanced Studies, Vienna); Schipper, Burkhard (University of CA, Davis) 
Abstract:  We define a generalized statespace model with interactive unawareness and probabilistic beliefs. Such models are desirable for potential applications of asymmetric unawareness. Applying our unawareness belief structures, we show that the common prior assumption is too weak to rule out speculative trade in all states. Yet, we prove a generalized "Nospeculativetrade" theorem according to which there can not be common certainty of strict preference to trade. Moreover, we prove a generalization of the "Noagreeingtodisagree" theorem. Finally, we show the existence of a universal unawareness belief type space. 
JEL:  C70 C72 D53 D80 D82 
Date:  2011–10 
URL:  http://d.repec.org/n?u=RePEc:ecl:ucdeco:118&r=gth 
By:  Conrads, Julian (University of Cologne); Irlenbusch, Bernd (University of Cologne) 
Abstract:  In his classic article "An Essay on Bargaining" Schelling (1956) argues that ignorance might actually be strength rather than weakness. We test and confirm Schelling's conjecture in a simple takeitorleave bargaining experiment where the proposer can choose between two possible offers. Option A always gives the proposer a higher payoff than option B. The payoff of the responder depends on the (randomly determined) state of nature, i.e., in state s2 payoffs of the two players are aligned while they are not in state s1. The responder is always informed about the actual state. The proposer knows the actual state in our first treatment but not in the second. We find that proposers indeed benefit from ignorance because the responders accept almost all offers (even the unfavorable ones) if the payoffs of the responder have not been transparent for the proposer. In additional treatments we investigate situations where the proposer can deliberately remain ignorant. One could assume that remaining ignorant on purpose would be punished by the responder at least if an unfavorable outcome results. Surprisingly, we find that strategically remaining ignorant tends to be beneficial for the proposer particularly if the responder does not know with certainty whether it was the proposer's intention to remain ignorant or whether it was not her intention. 
Keywords:  strategic ignorance, bargaining, intentions, experiment 
JEL:  C72 C78 C91 D63 D82 D83 
Date:  2011–10 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp6087&r=gth 
By:  Trautmann, S.T.; Kuilen, G. van de (Tilburg University, Center for Economic Research) 
Abstract:  In survey studies, probabilistic expectations about uncertain events are typically elicited by asking respondents for their introspective beliefs. If more complex procedures are feasible, beliefs can be elicited by incentive compatible revealed preference mechanisms (â€œtruth serumsâ€). Various mechanisms have been proposed in the literature, which differ in the degree to which they account for respondentsâ€™ deviations from expected value maximization. In this paper, we pit nonincentivized introspection against five truth serums, to elicit beliefs in a simple twoplayer game. We test the internal validity (additivity and predictive power for own behavior), and the external validity (predictive power for other playersâ€™ behavior, or accuracy) of each method. We find no differences among the truth serums. Beliefs from incentivized methods are better predictors of subjectsâ€™ own behavior compared to introspection. However, introspection performs equally well as the truth serums in terms of accuracy and additivity. 
Keywords:  belief measurement;subjective probability;scoring rules;outcome matching;probability matching;internal validity;external validity. 
JEL:  D81 C91 
Date:  2011 
URL:  http://d.repec.org/n?u=RePEc:dgr:kubcen:2011117&r=gth 
By:  Paolo Di Giannatale, Francesco Passarelli 
Abstract:  We study political distortions that emerge in situations where agents' political power is disproportionate with respect to their economic power. We provide a precise definition which adopts the same measure unit, the Shapley value, to evaluate both the economic and the political power. We show that usual weighted majority voting cannot prevent political distortions from emerging in a huge mass of situations. We propose an alternative voting method based on random assignments of voting rights. Agents are given chances to vote instead of weights. If chances are computed according to a specific formula, no political distortion occurs. As an application, we analyze the rotation voting system recently adopted by the European Central Bank. We find that this system yields an enormous amount of political distortion. Then we compute the voting chances that should be assigned to countries in order to eliminate it. 
Keywords:  Voting power, Economic power, Political distortions, Voting rules, Weighted votes, Shapley value, Shapley Shubik index, European Central Bank 
JEL:  C71 D71 D72 
Date:  2011–11 
URL:  http://d.repec.org/n?u=RePEc:slp:islawp:islawp40&r=gth 
By:  Etienne Billette De Villemeur (EQUIPPE  ECONOMIE QUANTITATIVE, INTEGRATION, POLITIQUES PUBLIQUES ET ECONOMETRIE  Université des Sciences et Technologies de Lille  Lille I); Richard Ruble (EMLYON RECHERCHE  EMLYON Business School, GATE Lyon SaintEtienne  Groupe d'analyse et de théorie économique  CNRS : UMR5824  Université Lumière  Lyon II  École Normale Supérieure de Lyon); Bruno Versaevel (EMLYON RECHERCHE  EMLYON Business School, GATE Lyon SaintEtienne  Groupe d'analyse et de théorie économique  CNRS : UMR5824  Université Lumière  Lyon II  École Normale Supérieure de Lyon) 
Abstract:  We characterize sequential (preemption) and simultaneous (coordination) equilibria, as well as jointvalue maximizing (cooperation) solutions, in a model of investment timing allowing for externalities in both flow pro...ts and investment costs. For two exante symmetric ...rms, either preemption or attrition occur depending on the size of the investment externality. Coordination is less likely with more discounting, as in a repeated game, and more likely with higher growth and volatility. Optimal cooperation involves either monopoly or duopoly investment, the latter being either symmetric or asymmetric. Finally, these characterizations are validated by applications to standard speci...cations of capacity accumulation and of R&D investment. In the former setup, coordination is likelier if installed capacities and lumpy investments are both large. With R&D input choices, if investment synergies are large, coordination and cooperation result in the same outcomes. 
Keywords:  Investment Timing; Real Options; Simultaneous Equilibrium; JointValue Maximization; Cooperation; Investment Externalities 
Date:  2011 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs00639471&r=gth 
By:  Bowen, Renee (Stanford University) 
Abstract:  I present a theory of optimal multilateral trade agreements with public political shocks. I first show that "forbearance" where one country withholds retaliation when its trading partner receives a shock is a feature of an optimal agreement. This provides a rationale for countries not acting on retaliatory rights granted under GATT. Second I show that there is a limit to forbearance allowable in a selfenforcing agreement. This limit is increasing in the number of countries in the agreement, increasing in the common discount factor, and increasing in the size of the export sector. 
JEL:  C73 D74 F10 
Date:  2011–11 
URL:  http://d.repec.org/n?u=RePEc:ecl:stabus:2085&r=gth 
By:  Pearson, Matthew (University of CA, Davis); Schipper, Burkhard C. (University of CA, Davis) 
Abstract:  In an experiment using twobidder firstprice sealed bid auctions with symmetric independent private values and 400 subjects, we scan also the right hand of each subject. We study how the ratio of the length of the index and ring fingers (2D:4D) of the right hand, a measure of prenatal hormone exposure, is correlated with bidding behavior and total profits. 2D:4D has been reported to predict competitiveness in sports competition (Manning and Taylor, 2001, and Hoenekopp, Manning, and Mueller, 2006), risk aversion in lottery tasks (Dreber and Hoffman, 2007, Garbarino et al., 2010), and the average profitability of highfrequency traders in financial markets (Coates, Gurnell, and Rustichini, 2009). We do not find any significant correlation between 2D:4D on either bidding or profits. However, there might be racial differences in the correlation between 2D:4D and bidding and profits. 
JEL:  C72 C91 C92 D44 D81 D87 
Date:  2011–10 
URL:  http://d.repec.org/n?u=RePEc:ecl:ucdeco:119&r=gth 
By:  Pearson, Matthew (University of CA, Davis); Schipper, Burkhard C. (University of CA, Davis) 
Abstract:  In an experiment using twobidder firstprice sealed bid auctions with symmetric independent private values and 400 participants, we collected information on the female participants' menstrual cycles and the use of hormonal contraceptives. We find that naturally cycling women bid significantly higher than men and earn significantly lower profits than men except during the midcycle when fecundity is highest. We suggest an evolutionary hypothesis according to which women are predisposed by hormones to generally behave more riskily during their fecund phase of their menstrual cycle in order to increase the probability of conception, quality of offspring, and genetic variety. We also find that women on hormonal contraceptives bid significantly higher and earn substantially lower profits than men. This may be due to progestins contained in hormonal contraceptives or a selection effect. We discuss how our study differs from Chen, Katuscak, and Ozdenoren (2009). 
JEL:  C72 C91 C92 D44 D81 D87 
Date:  2011–11 
URL:  http://d.repec.org/n?u=RePEc:ecl:ucdeco:1110&r=gth 