
on Game Theory 
Issue of 2008‒11‒04
seventeen papers chosen by Laszlo A. Koczy Budapest Tech and Maastricht University 
By:  Michel Grabisch (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I); Agnieszka Rusinowska (GATE  Groupe d'analyse et de théorie économique  CNRS : UMR5824  Université Lumière  Lyon II  Ecole Normale Supérieure Lettres et Sciences Humaines) 
Abstract:  In the paper, we study a relation between command games proposed by Hu and Shapley and an influence model. We show that our framework of influence is more general than the framework of the command games. We define several influence functions which capture the command structure. These functions are compatible with the command games, in the sense that each commandable player for a coalition in the command game is a follower of the coalition under the command influence function. For some influence functions we define the command games such that the influence functions are compatible with these games. We show that not for all influence functions such command games exist. Moreover, we propose a more general definition of the influence index and show that some power indices, which can be used in the command games, coincide with some expressions of the weighted influence indices. We show exact relations between an influence function and a follower function, between a command game and commandable players, and between influence functions and command games. An example of the Confucian model of society is broadly examined. 
Keywords:  Banzhaf index ; Coleman indices ; command game ; follower of a coalition ; influence function ; influence indices ; ShapleyShubik index 
Date:  2008 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:halshs00269084_v1&r=gth 
By:  Kris De Jaegher 
Abstract:  As shown by Rubinstein (1989, AER), in the twoplayer electronic mail game, players are better off if the extent to which they can check each other’s information, check each other’s information about each other’s information, etc., is limited. This paper investigates to what extent this result extends to the multiplayer electronic mail game. It is shown that, contrary to the twoplayer game, the multiplayer game has a plethora of equilibria. If players play inefficient equilibria where they require a specific communication network to be established in order to achieve collective action, then Rubinstein’s results extend. However, contrary to the twoplayer game, the multiplayer game also has equilibria where players find many alternative communication networks sufficient to undertake collective action. If players play such equilibria, then contrary to what is the case in the twoplayer electronic mail game they can become better off with more information. 
Keywords:  MultiPlayer Electronic Mail Game, Collective Action, Communication Networks. 
JEL:  D82 D85 D71 
Date:  2008–10 
URL:  http://d.repec.org/n?u=RePEc:use:tkiwps:0831&r=gth 
By:  Reinoud Joosten; Berend Roorda 
Abstract:  We introduce a new kind of projection dynamics by employing a rayprojection both locally and globally. By global (local) we mean a projection of a vector (close to the unit simplex) unto the unit simplex along a ray through the origin. Using a correspondence between local and global rayprojection dynamics we prove that every interior evolutionarily stable strategy is an asymptotically stable fixed point. We also show that every strict equilibrium is an evolutionarily stable state and an evolutionarily stable equilibrium. Then, we employ several projections on a wider set of functions derived from the payoff structure. This yields an interesting class of socalled generalized projection dynamics which contains bestresponse, logit, replicator, and BrownVonNeumann dynamics among others. 
Keywords:  evolutionary game theory, projection dynamics, orthogonal projection, ray projection, asymptotical and evolutionary stability Length 27 pages 
JEL:  A12 C62 C72 C73 D83 
Date:  2008–10 
URL:  http://d.repec.org/n?u=RePEc:esi:evopap:200811&r=gth 
By:  Michel Grabisch (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I); Pedro Miranda (Universidad Complutense de Madrid  Universidad Complutense de Madrid) 
Abstract:  The core of a game $v$ on $N$, which is the set of additive games $\phi$ dominating $v$ such that $\phi(N)=v(N)$, is a central notion in cooperative game theory, decision making and in combinatorics, where it is related to submodular functions, matroids and the greedy algorithm. In many cases however, the core is empty, and alternative solutions have to be found. We define the $k$additive core by replacing additive games by $k$additive games in the definition of the core, where $k$additive games are those games whose M\"obius transform vanishes for subsets of more than $k$ elements. For a sufficiently high value of $k$, the $k$additive core is nonempty, and is a convex closed polyhedron. Our aim is to establish results similar to the classical results of Shapley and Ichiishi on the core of convex games (corresponds to Edmonds' theorem for the greedy algorithm), which characterize the vertices of the core. 
Date:  2008 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:hal00321625_v1&r=gth 
By:  Michel Grabisch (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I); Agnieszka Rusinowska (GATE  Groupe d'analyse et de théorie économique  CNRS : UMR5824  Université Lumière  Lyon II  Ecole Normale Supérieure Lettres et Sciences Humaines) 
Abstract:  In the paper, we introduce and study generalized weighted influence indices of a coalition on a player, where players have an ordered set of possible actions. Each player has an inclination to choose one of the actions. Due to influence of a coalition of other players, a final decision of the player may be different from his original inclination. An influence in such situations is measured by the general weighted influence index. In a particular case, the decision of the player may be closer to the inclination of the influencing coalition than his inclination was. The weighted influence index which captures such a case is called the positive weighted influence index. We also consider the negative weighted influence index, where a final decision of the player goes farther away from the inclination of the influencing coalition. Some special cases of the weighted influence indices, called a possibility influence index and an equidistributed influence index, are also defined. We consider different influence functions and study their properties. A set of followers and a set of a conditional followers of a given coalition are defined, and their properties are analyzed. We define the concepts of success, decisiveness, luck, and failure for the multichoice model of influence. 
Keywords:  decisiveness ; follower of a coalition ; influence function ; influence indices ; success 
Date:  2008 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:halshs00260863_v1&r=gth 
By:  Joseph Abdou (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); Hans Keiding (University of Copenhagen  Institute of Economics) 
Abstract:  We introduce a description of the power structure which is inherent in a strategic game form using the concept of an interaction sheaf. The latter assigns to each open set of outcomes a set of interaction arrays, specifying the changes that coalitions can make if outcome belongs to this open set. The interaction sheaf generalizes the notion of effectivity functions which has been widely used in implementation theory, taking into consideration that changes in outcome may be sustained not only by single coalitions but possibly by several coalitions, depending on the underlying strategy choices. Also, it allows us to consider game forms with not necessarily finite sets of outcomes, generalizing the results on solvability of game forms obtained in the finite case in Abdou and Keiding (2003). 
Keywords:  Nash equilibrium, strong equilibrium, solvability, effectivity, acyclicity. 
Date:  2008–04 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:halshs00289299_v1&r=gth 
By:  Philippe Bich (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I) 
Abstract:  In a recent but well known paper, Reny has proved the existence of Nash equilibria for compact and quasiconcave games, with possibly discontinuous payoff functions. In this paper, we prove that the quasiconcavity assumption in Reny's theorem can be weakened: roughly, we introduce a measure allowing to localize the lack of quasiconcavity; this allows to refine the analysis of equilibrium existence 
Keywords:  Nash equilibrium, existence, discontinuous games, non quasiconcave 
Date:  2008–09–20 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:halshs00323348_v1&r=gth 
By:  RÃ¼bbelke, Dirk T.G.; Finus, Michael 
Abstract:  Several studies found ancillary benefits of environmental policy to be of considerable size. These additional private benefits imply not only higher cooperative but also noncooperative abatement targets. However, beyond these largely undisputed important quantitative effects, there are qualitative and strategic implications associated with ancillary benefits: climate policy is no longer a pure but an impure public good. In this paper, we investigate these implications in a setting of noncooperative coalition formation. In particular, we address the following questions. 1) Do ancillary benefits increase participation in international environmental agreements? 2) Do ancillary benefits raise the success of these treaties in welfare terms? 
Keywords:  impure public goods; game theory; coalition formation; climate policy; ancillary benefits 
Date:  2008–07 
URL:  http://d.repec.org/n?u=RePEc:stl:stledp:200813&r=gth 
By:  Dirk Engelmann; Urs Fischbacher 
Abstract:  We study indirect reciprocity and strategic reputation building in an experimental helping game. At any time only half of the subjects can build a reputation. This allows us to study both pure indirect reciprocity that is not contaminated by strategic reputation building and the impact of incentives for strategic reputation building on the helping rate. We find that pure indirect reciprocity exists, but also that the helping decisions are substantially a!ected by strategic considerations. We find that the behavioral pattern can best be captured by nonselfish preferences as assumed by reciprocity models. Finally, we find that strategic do better than nonstrategic players and nonreciprocal do better than reciprocal players, casting doubt on previously proposed evolutionary explanations for indirect reciprocity. 
Keywords:  indirect reciprocity, reputation, experimental economics 
Date:  2008 
URL:  http://d.repec.org/n?u=RePEc:twi:respas:0034&r=gth 
By:  Takako FujiwaraGreve (Faculty of Economics, Keio University); Masahiro OkunoFujiwara (Faculty of Economics, University of Tokyo) 
Abstract:  Ordinary repeated games do not apply to real societies where one can cheat and escape from partners. We formulate a model of endogenous relationships that a player can unilaterally end and start with a randomlyassigned new partner with no information flow. Focusing on twoperson, twoaction Prisoner's Dilemma, we show that the endogenous duration of partnerships generates a significantly different evolutionary stability structure from ordinary random matching games. Monomorphic equilibria require initial trustbuilding, while a polymorphic equilibrium includes earlier cooperators than any strategy in monomorphic equilibria and is thus more efficient. This is due to the nonlinearity of average payoffs.Length: 37pages 
Date:  2008–10 
URL:  http://d.repec.org/n?u=RePEc:tky:fseres:2008cf599&r=gth 
By:  Catherine Bros (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I) 
Abstract:  The aim of this paper is to provide a detailed analysis of the process of segregation formation. The claim is that segregation does not originate from prejudice or exogenous psychological factors. Rather it is the product of strategic interactions among social groups in a setting where one group has captured power. While using a model featuring random matching and repeated games, it is shown that whenever one group seizes power, members of other groups will perceive additional value in forging long term relationships with the mighty. They will systematically cooperate with the latter either because it is in their interest to do so or because they do not have other choice. The mighty natural response to this yearning to cooperate is to refuse intergroup relationships. The dominated group will best reply to this new situation by in turn rejecting the relationships and a segregation equilibrium emerges. Segregation stems from the systematic cooperation by one group with another. However, not all societies that have experienced power captures converge towards segregation. It is shown that the proportion of individuals that are actually powerful within the mighty group determines convergence towards segregation. 
Keywords:  Segration, discrimination, power, caste, repeated games, prisoner's dilemma, clubs, status, social organizations. 
Date:  2008–01 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:halshs00204974_v1&r=gth 
By:  James Bono 
Abstract:  Casual observation reveals that groups of people interact on many levels simultane ously. Examples include political party formation and interaction; the interaction of ¯rms in research consortia; and labor union and confederation formation. In this paper, a model of hierarchical group structures is developed. The model generalizes the existing coalitional theory in several ways and reveals a new connection between characteristic and partition function theories; that they are both valuable components of an overall theory. The stability concept that emerges is called the core of cores. Several results are presented, including necessary and su±cient conditions for the existence of the core of cores and a theorem that demonstrates the relationship between the cores of each level of the organizational structure and the core of cores. The results establish that stability can arise from any combination of stable and unstable components, and suggest a rethinking of existing coalitional models, taking into account the e®ect of \nearby" games. The framework developed here has immediate applications to various topics in political econ omy and industrial organization, such as representative voting and corporate mergers. 
Keywords:  The Core, Complexity in Game Theory, Hierarchies of Groups 
JEL:  C62 C71 C79 D72 
Date:  2008–09 
URL:  http://d.repec.org/n?u=RePEc:amu:wpaper:1808&r=gth 
By:  Philippe Bich (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I) 
Abstract:  One answers to an open question of Herings et al. (2008), by proving that their fixed point theorem for discontinuous functions works for mappings defined on convex compact subset of $\R^n$, and not only polytopes. This fixed point theorem can be applied to the problem of Nash equilibrium existence in discontinuous games. 
Keywords:  fixed point theorem; discontinuity; nash equilibrium 
Date:  2008–02 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:halshs00265464_v1&r=gth 
By:  Joseph Abdou (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) 
Abstract:  We study the structure of unstable local effectivity functions defined for n players and p alternatives. A stability index based on the notion of cycle is introduced. In the particular case of simple games, the stability index is closely related to the Nakamura Number. In general it may be any integer between 2 and p. We prove that the stability index for maximal effectivity functions and for maximal local effectivity functions is either 2 or 3. 
Keywords:  Effectivity function, local effectivity function, acyclicity, stability index, Nakamura Number, acyclicity. 
Date:  2008–07 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:halshs00331223_v1&r=gth 
By:  James W. Boudreau (University of Connecticut) 
Abstract:  Agents on the same side of a twosided matching market (such as the marriage or labor market) compete with each other by making selfenhancing investments to improve their worth in the eyes of potential partners. Because these expenditures generally occur prior to matching, this activity has come to be known in recent literature (Peters, 2007) as premarital investment. This paper builds on that literature by considering the case of sequential premarital investment, analyzing a matching game in which one side of the market invests first, followed by the other. Interpreting the first group of agents as workers and the other group as firms, the paper provides a new perspective on the incentive structure that is inherent in labor markets. It also demonstrates that a positive rate of unemployment can exist even in the absence of matching frictions. Policy implications follow, as the prevailing set of equilibria can be altered by restricting entry into the workforce, providing unemployment insurance, or subsidizing premarital investment. 
Keywords:  Matching, premarital investment, unemployment. 
JEL:  C78 H30 E24 
Date:  2008–10 
URL:  http://d.repec.org/n?u=RePEc:uct:uconnp:200845&r=gth 
By:  Julio Davila (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); Jan Eeckhout (University of Pennsylvania  Department of Economics); César Martinelli (Centro de Investigacion Economica  Instituto Tecnologico Autonomo) 
Abstract:  In a simple public good economy, we propose a natural bargaining procedure whose equilibria converge to Lindahl allocations as the cost of bargaining vanishes. The procedure splits the decision over the allocation in a decision about personalized prices and a decision about output levels for the public good. Since this procedure does not assume pricetaking behavior, it provides a strategic foundation for the personalized taxes inherent to the Lindahl solution to the public goods problem. 
Keywords:  Public goods, bargaining, alternating offers. 
Date:  2008–06 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:halshs00289435_v1&r=gth 
By:  Thibault Gajdos (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); Takashi Hayashi (Department of Economics, University of Texas at Austin  University of Texas at Austin); JeanMarc Tallon (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); JeanChristophe Vergnaud (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) 
Abstract:  This paper presents an axiomatic model of decision making under uncertainty which incorporates objective but imprecise information. Information is assumed to take the form of a probabilitypossibility set, that is, a set $P$ of probability measures on the state space. The decision maker is told that the true probability law lies in $P$ and is assumed to rank pairs of the form $(P,f) $ where $f$ is an act mapping states into outcomes. Thekey representation result delivers maxmin expected utility where the min operator ranges over a set of probability priors just as in the maxmin expected utility (MEU) representation result of \cite{GILB/SCHM/89}. However, unlike the MEU representation, the representation here also delivers a mapping, $\varphi$, which links the probabilitypossibility set, describing the availableinformation, to the set of revealed priors. The mapping $\varphi$ is shown to represent the decision maker's attitude to imprecise information: under our axioms, the set of representation priors is constituted as a selection from the probabilitypossibility set.This allows both expected utility when the selected set is a singleton and extreme pessimism when the selected set is the same as the probabilitypossibility set, i.e. , $\varphi$ is the identity mapping. We define a notion of comparative imprecision aversion and show it is characterized by inclusion of the sets of revealedprobability distributions, irrespective of the utility functions that capture risk attitude. We also identify an explicit attitude toward imprecision that underlies usual hedging axioms. Finally, we characterize, under extra axioms, a more specific functional form, in which the set of selected probability distributions is obtained by (i) solving for the ``mean value'' of the probabilitypossibility set, and (ii) shrinking the probabilitypossibility set toward the mean value to a degree determined by preferences. 
Keywords:  precise information, imprecision aversion, multiple priors, Steiner point. 
Date:  2008–05 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:halshs00177378_v1&r=gth 