
on Game Theory 
By:  Andrei Dubovik (Erasmus University Rotterdam); Alexei Parakhonyak (Erasmus University Rotterdam) 
Abstract:  We consider a dynamic (differential) game with three players competing against each other. Each period each player can allocate his resources so as to direct his competition towards particular rivals  we call such competition selective. The setting can be applied to a wide variety of cases: competition between firms, competition between political parties, warfare. We show that if the players are myopic, the weaker players eventually loose the game to their strongest rival. Vice versa, if the players value their future payoffs high enough, each player concentrates more on fighting his strongest opponent. Consequently, the weaker players grow stronger, the strongest player grows weaker and eventually all the players converge and remain in the game. 
Keywords:  selective competition; dynamic oligopolies; differential games 
JEL:  C73 D43 
Date:  2009–08–12 
URL:  http://d.repec.org/n?u=RePEc:dgr:uvatin:20090072&r=gth 
By:  Jung, Hanjoon Michael 
Abstract:  Crawford and Sobel (1982) developed a model of strategic information transmission in which a betterinformed sender sends a possibly informative signal to a decisionmaking receiver and studied how strategically transmitted information is related to the analogy between the two players' interests. They adopted the Bayesian Nash equilibrium as their equilibrium concept and showed that the signal by the sender, the transmitted information, is more informative in paretosuperior equilibrium when the players' interests are more analogous. Their analyses, however, are not complete in that they analyzed the model based on partial consideration of the players' behavior, mixed behavior of the sender and pure behavior of the receiver. In the present study, we attempt to complete their analyses by analyzing the model based on full consideration of the players' behavior, both pure and mixed behavior. We adopt the Nash equilibrium as our equilibrium concept and conclude that results in our complete analyses are similar to the results in Crawford and Sobel (1982). 
Keywords:  Nash equilibrium; Signaling Game; Cheap Talk 
JEL:  C72 
Date:  2009–09 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:17115&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, a yesno model of inﬂuence is generalized to a multichoice framework. We introduce and study weighted inﬂuence indices of a coalition on a player in a social network, where players have an ordered set of possible actions. Each player has an inclination to choose one of the actions. Due to mutual inﬂuence among players, the ﬁnal decision of each player may be different from his original inclination. In a particular case, the decision of the player is closer to the inclination of the inﬂuencing coalition than his inclination was, i.e., the distance between the inclinations of the player and of the coalition is greater than the distance between the decision of the player and the inclination of the coalition in question. The weighted inﬂuence index which captures such a case is called the weighted positive inﬂuence index. We also consider the weighted negative inﬂuence index, where the ﬁnal decision of the player goes farther away from the inclination of the coalition. We consider several inﬂuence functions deﬁned in the generalized model of inﬂuence and study their properties. The concept of a follower of a given coalition, and its particular case, a perfect follower, are deﬁned. The properties of the set of followers are analyzed. 
Keywords:  weighted positive inﬂuence index; weighted negative inﬂuence index; inﬂuence function; follower of a coalition; perfect follower; kernel 
Date:  2009 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs00406439_v1&r=gth 
By:  Michel Grabisch (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I, LIP6  Laboratoire d'Informatique de Paris 6  CNRS : UMR7606  Université Pierre et Marie Curie  Paris VI); 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 this paper, we study a model of influence in a social network. It is assumed that each player has an inclination to say YES or NO which, due to influence of other players, may be different from the decision of the player. The point of departure here is the concept of the HoedeBakker index—the notion which computes the overall decisional ‘power' of a player in a social network. The main drawback of the HoedeBakker index is that it hides the actual role of the influence function, analyzing only the final decision in terms of success and failure. In this paper, we separate the influence part from the group decision part, and focus on the description and analysis of the influence part. We propose among other descriptive tools a definition of a (weighted) influence index of a coalition upon an individual. Moreover, we consider different influence functions representative of commonly encountered situations. Finally, we propose a suitable definition of a modified decisional power. 
Keywords:  Influence function ; Influence index ; Decisional power ; Social network 
Date:  2009 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs00308741_v1&r=gth 
By:  Eyal Winter; Ignacio GarciaJurado; Jose MendezNaya; Luciano MendezNaya 
Abstract:  We introduce emotions into an equilibrium notion. In a mental equilibrium each player "selects" an emotional state which determines the player's preferences over the outcomes of the game. These preferences typically differ from the players' material preferences. The emotional states interact to play a Nash equilibrium and in addition each player's emotional state must be a best response (with respect to material preferences) to the emotional states of the others. We discuss the concept behind the definition of mental equilibrium and show that this behavioral equilibrium notion organizes quite well the results of some of the most popular experiments in the experimental economics literature. We shall demonstrate the role of mental equilibrium in incentive mechaisms and will discuss the concept of collective emotions, which is based on the idea that players can coordinate their emotional states. 
Date:  2009–09 
URL:  http://d.repec.org/n?u=RePEc:huj:dispap:dp521&r=gth 
By:  Brekke, Kjell Arne (Dept. of Economics, University of Oslo); Hauge, Karen Evely (Dept. of Economics, University of Oslo); Lind, Jo Thori (Dept. of Economics, University of Oslo); Nyborg, Karine (Dept. of Economics, University of Oslo) 
Abstract:  In public good games, voluntary contributions tend to start o high and decline as the game is repeated. If high contributors are matched, however, contributions tend to stay high. We propose a formalization predicting that high contributors will selfselect into groups committed to charitable giving. Testing this experimentally, we let subjects choose between two group types, where one type donate a xed amount to a charity. Contributions in these groups stayed high, whereas contributions in the other groups showed the well known declining pattern. One implication is that corporate social responsibility may attract more responsible employees. 
Keywords:  Altruism; conditional cooperation; selfselection 
JEL:  D11 D12 D64 H41 
Date:  2009–04–17 
URL:  http://d.repec.org/n?u=RePEc:hhs:osloec:2009_008&r=gth 
By:  Robert J. Aumann 
Abstract:  "Game Engineering" deals with the application of game theoretic methods to interactive situations or systems in which the rules are well defined, or where the designer can himself specify the rules. This talk, which addressed a businessschool audience with no specific knowledge of game theory, describes five examples of game engineering: two dealing with auctions, two with traffic systems, and one with arbitration. At the end of the talk there was a Q & A session, which, too, is recorded here. 
Date:  2009–09 
URL:  http://d.repec.org/n?u=RePEc:huj:dispap:dp518&r=gth 
By:  Johannes Horner (Cowles Foundation, Yale University); Larry Samuelson (Cowles Foundation, Yale University) 
Abstract:  We examine a repeated interaction between an agent, who undertakes experiments, and a principal who provides the requisite funding for these experiments. The agent's actions are hidden, and the principal, who makes the offers, cannot commit to future actions. We identify the unique Markovian equilibrium (whose structure depends on the parameters) and characterize the set of all equilibrium payoffs, uncovering a collection of nonMarkovian equilibria that can Pareto dominate and reverse the qualitative properties of the Markovian equilibrium. The prospect of lucrative continuation payoffs makes it more expensive for the principal to incentivize the agent, giving rise to a dynamic agency cost. As a result, constrained efficient equilibrium outcomes call for nonstationary outcomes that frontload the agent's effort and that either attenuate or terminate the relationship inefficiently early. 
Keywords:  Experimentation, Learning, Agency, Dynamic agency, Venture Capital, Repeated principalagent problem 
JEL:  D8 L2 
Date:  2009–09 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:1726&r=gth 
By:  Rudolf Berghammer (ComputerAided Program Development  Institute of Computer Science  ChristianAlbrechtsUniversität, Kiel); Agnieszka Rusinowska (GATE  Groupe d'analyse et de théorie économique  CNRS : UMR5824  Université Lumière  Lyon II  Ecole Normale Supérieure Lettres et Sciences Humaines); Harrie De Swart (Faculteit WijsbegeerteLogica en taalanalyse  Universiteit van Tilburg) 
Abstract:  A stable government is by deﬁnition not dominated by any other government. However, it may happen that all governments are dominated. In graphtheoretic terms this means that the dominance graph does not possess a source. In this paper we are able to deal with this case by a clever combination of notions from different ﬁelds, such as relational algebra, graph theory and social choice theory, and by using the computer support system RelView for computing solutions and visualizing the results. Using relational algorithms, in such a case we break all cycles in each initial strongly connected component by removing the vertices in an appropriate minimum feedback vertex set. In this way we can choose a government that is as close as possible to being undominated. To achieve unique solutions, we additionally apply the majority ranking recently introduced by Balinski and Laraki. The main parts of our procedure can be executed using the RelView tool. Its sophisticated implementation of relations allows to deal with graph sizes that are sufficient for practical applications of coalition formation. 
Keywords:  Graph theory; RelView; relational algebra; dominance; stable government 
Date:  2009 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs00406460_v1&r=gth 
By:  Itzhak Gilboa (Tel Aviv University); Larry Samuelson (Cowles Foundation, Yale University) 
Abstract:  This paper examines circumstances under which subjectivity enhances the effectiveness of inductive reasoning. We consider a game in which Fate chooses a data generating process and agents are characterized by inference rules that may be purely objective (or databased) or may incorporate subjective considerations. The basic intuition is that agents who invoke no subjective considerations are doomed to "overfit" the data and therefore engage in ineffective learning. The analysis places no computational or memory limitations on the agents  the role for subjectivity emerges in the presence of unlimited reasoning powers. 
Keywords:  Induction, Simplicity, Bayesian learning 
JEL:  D8 C0 
Date:  2009–08 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:1725&r=gth 