
on Game Theory 
Issue of 2009‒06‒17
thirteen papers chosen by Laszlo A. Koczy Budapest Tech and Maastricht University 
By:  Heller, Yuval 
Abstract:  We prove that every undiscounted multiplayer stopping game in discrete time admits an approximate correlated equilibrium. Moreover, the equilibrium has five appealing properties: (1) “Tremblinghand” perfectness  players do not use noncredible threats; (2) Normalform correlation  communication is required only before the game starts; (3) Uniformness  it is an approximate equilibrium in any long enough finitehorizon game and in any discounted game with high enough discount factor; (4) Universal correlation device the device does not depend on the specific parameters of the game. (5) Canonical  the signal each player receives is equivalent to the strategy he plays in equilibrium. 
Keywords:  stochastic games; stopping games; correlated equilibrium; perfect equilibrium; Ramsey Theorem. 
JEL:  C73 
Date:  2009–06–10 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:15646&r=gth 
By:  Joseph Abdou (Centre d'Economie de la Sorbonne  Paris School of Economics) 
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:  Stability index, acyclicity, strong Nash equilibrium, core, solvability, consistency, simple game, effectivity function. 
JEL:  C70 D71 
Date:  2009–01 
URL:  http://d.repec.org/n?u=RePEc:mse:cesdoc:09041&r=gth 
By:  Srihari Govindan; Robert Wilson 
Date:  2009–05–31 
URL:  http://d.repec.org/n?u=RePEc:cla:levarc:814577000000000231&r=gth 
By:  Jung, Hanjoon Michael 
Abstract:  We propose a complete version of the sequential equilibrium (CSE) and its alternative solution concept (WCSE) for general finiteperiod games with observed actions. The sequential equilibrium (SE) is not a complete solution concept in that it might not be a Nash equilibrium in the general games that allow a continuum of types and strategies. The CSE is always a Nash equilibrium and is equivalent to the SE in finite games. So, the CSE is a complete solution concept in the general games as a version of the SE. The WCSE is a weak, but simple version of the CSE. It is also a complete solution concept and functions as an alternative solution concept to the CSE. Their relation with converted versions of the perfect equilibrium and the perfect Bayesian equilibrium are discussed 
Keywords:  Complete Belief; Complete Sequential Equilibirum; Finiteperiod game; Solution Concept; Sequential Convergency; Sequential Equilibrium. 
JEL:  C72 
Date:  2009–05–26 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:15443&r=gth 
By:  Bernard De Meyer (Centre d'Economie de la Sorbonne); Ehud Lehrer (School of Mathematical Sciences  Tel Aviv University); Dinah Rosenberg (LAGA Institut Galilée  Université Paris 13) 
Abstract:  In a Bayesian game some players might receive a noisy signal regarding the specific game actually being played before it starts. We study zerosum games where each player receives a partial information about his own type and no information about that of the other player and analyze the impact the signals have on the payoffs. It turns out that the functions that evaluate the value of information share two property. The first is Blackwell monotonicity, which means that each player gains from knowing more. The second is concavity on the space of conditional probabilities. 
Keywords:  Value of information, Blackwell monotonicity, concavity. 
JEL:  C72 C73 D80 D82 D83 
Date:  2009–05 
URL:  http://d.repec.org/n?u=RePEc:mse:cesdoc:09035&r=gth 
By:  De Marco, Giuseppe; Romaniello, Maria 
Abstract:  In Hart and Kurz (1983), stability and formation of coalition structures has been investigated in a noncooperative framework in which the strategy of each player is the coalition he wishes to join. However, given a strategy profile, the coalition structure formed is not unequivocally determined. In order to solve this problem, they proposed two rules of coalition structure formation: the $\gamma$ and the $\delta$ models. \par In this paper we look at evolutionary games arising from the $\gamma$ model for situations in which each player can choose mixed strategies and has vague expectations about the formation rule of the coalitions in which is not involved; players determine at every instant their strategies and we study how, for every player, subjective beliefs on the set of coalition structures evolve coherently to the strategic choices. Coherency is regarded as a viability constraint for the differential inclusions describing the evolutionary game. Therefore, we investigate viability properties of the constraints and characterize velocities of pairs belief/strategies which guarantee that coherency of beliefs is always satisfied. Finally, among many coherent belief revisions (evolutions), we investigate those characterized by minimal change and provide existence results. 
Keywords:  Coalition formation; coherent beliefs; differential inclusions; viability theory; minimal change belief revision 
JEL:  D71 C71 D83 C72 C73 
Date:  2008–03–26 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:14725&r=gth 
By:  Du, Songzi 
Abstract:  In this note we characterize the strategic implication of intrinsic correlation, introduced by Brandenburger and Friedenberg (2008), in the subjective correlated equilibrium setting of a complete information game. Intrinsic correlation restricts correlation devices to variables within the game, i.e. players's beliefs (and higher order beliefs) about each other's strategies, in contrast to signals or sunspots from the "outside." The characterization is a strengthening of bestresponse set with an injectivity condition for a certain subset identified by an iterative procedure. We also give an iterative procedure, analogous to the iterated removals of dominated strategies, that arrives at strategies consistent with our characterization, which always exist. 
Keywords:  game theory; correlated equilibrium; rationalizability; intrinsic correlation; higher order beliefs; redundant types; epistemics 
JEL:  C70 C72 
Date:  2008–12–08 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:12698&r=gth 
By:  Victor C. Domansky (St. Petersburg Institute for Economics and Mathematics  Russian Academy of Sciences); Victoria L. Kreps (St. Petersburg Institute for Economics and Mathematics  Russian Academy of Sciences) 
Abstract:  This paper is concerned with multistage bidding models introduced by De Meyer and Moussa Saley (2002) to analyze the evolution of the price system at finance markets with asymmetric information. The zerosum repeated games with incomplete information are considered modeling the bidding with countable sets of possible prices and admissible bids. It is shown that, if the liquidation price of a share has a finite variance, then the sequence of values of nstep games is bounded and converges to the value of the game with infinite number of steps. We construct explicitly the optimal strategies for this game. The optimal strategy of Player 1 (the insider) generates a symmetric random walk of posterior mathematical expectations of liquidation price with absorption. The expected duration of this random walk is equal to the initial variance of liquidation price. The guaranteed total gain of Player 1 (the value of the game) is equal to this expected duration multiplied with the fixed gain per step. 
Keywords:  Multistage bidding, asymmetric information, repeated games, optimal strategy. 
JEL:  C73 D82 D44 
Date:  2009–01 
URL:  http://d.repec.org/n?u=RePEc:mse:cesdoc:09040&r=gth 
By:  Angelo Antoci (Department of Economics, University of Sassari); Antonio Gay (University of Florence); Massimiliano Landi (School of Economics, Singapore Management University); Pier Luigi Sacco (IUAV, Venice) 
Abstract:  We consider a deterministic evolutionary model where players form expectations about future play. Players are not fully rational and have expectations that change over time in response to current payoffs and feedback from the past. We provide a complete characterization of the qualitative dynamics so induced for a two strategies population game,and relate our findings to standard evolutionary dynamics and equilibrium selection when agents have rational forward looking expectations 
Keywords:  evolutionary games; dynamic systems; bounded rationality 
JEL:  C73 
Date:  2007–12 
URL:  http://d.repec.org/n?u=RePEc:siu:wpaper:252007&r=gth 
By:  Joseph Abdou (Centre d'Economie de la Sorbonne  Paris School of Economics) 
Abstract:  A power system is modeled by an interaction form, the solution of which is called a settlement. By stability we mean the existence of some settlement for any preference profile. Like in other models of power structure, instability is equivalent to the existence of a cycle. Structural properties of the system like maximality, regularity, superadditivity and exactness are defined and used to determine the type of instability that may affect the system. A stability index is introduced. Loosely speaking this index measures the difficulty of the emergence of configurations that produce a deadlock. As applications we have a characterization of solvable game forms, an analysis of the structure of their instability and a localization of their stability index in case where solvability fails. 
Keywords:  Interaction form, effectivity function, stability index, Nash equilibrium, strong equilibrium, solvability, acyclicity, Nakamura number, collusion. 
JEL:  C70 D71 
Date:  2009–05 
URL:  http://d.repec.org/n?u=RePEc:mse:cesdoc:09042&r=gth 
By:  Michi Nishihara (Graduate School of Economics, Osaka University) 
Abstract:  This paper derives a preemptive equilibrium in strategic investment in alternative projects. The problem is formulated in a real options model with a multidimensional state variable that represents projectspecific uncertainty. The proposed method enables us to evaluate the value of potential alternatives. The results not only extend previous studies with a onedimensional state variable but also reveal new findings. Preemptive investment takes place earlier and the project value becomes lower if the numbers of both firms and projects increase by the same amount. Interestingly, a strong correlation among profits from projects, unlike in a monopoly, plays a positive role in moderating preemptive competition. 
Keywords:  strategic real options, preemption, alternative projects, stopping game. 
JEL:  C73 G13 G31 
Date:  2009–06 
URL:  http://d.repec.org/n?u=RePEc:osk:wpaper:0916&r=gth 
By:  Karl H. Schlag; Andriy Zapechelnyuk 
Date:  2009–06–08 
URL:  http://d.repec.org/n?u=RePEc:cla:levarc:814577000000000259&r=gth 
By:  Dieter Balkenborg; Josef Hofbauer; Christoph Kuzmics 
Date:  2009–06–08 
URL:  http://d.repec.org/n?u=RePEc:cla:levarc:814577000000000248&r=gth 