nep-gth New Economics Papers
on Game Theory
Issue of 2009‒06‒17
thirteen papers chosen by
Laszlo A. Koczy
Budapest Tech and Maastricht University

  1. Perfect correlated equilibria in stopping games By Heller, Yuval
  2. A Stability Index for Local Effectivity Functions. By Joseph Abdou
  3. Axiomatic Equilibrium Selection for Generic two-player games By Srihari Govindan; Robert Wilson
  4. Complete Sequential Equilibrium and Its Alternative By Jung, Hanjoon Michael
  5. Evaluating information in zero-sum games with incomplete information on both sides. By Bernard De Meyer; Ehud Lehrer; Dinah Rosenberg
  6. Evolution of Coalition Structures under Uncertainty By De Marco, Giuseppe; Romaniello, Maria
  7. A Note on Intrinsic Correlation By Du, Songzi
  8. Repeated games with asymmetric information and random price fluctuations at finance markets : the case of countable state space. By Victor C. Domansky; Victoria L. Kreps
  9. Global Analysis of an Expectations Augmented Evolutionary Dynamics By Angelo Antoci; Antonio Gay; Massimiliano Landi; Pier Luigi Sacco
  10. The Structure of Unstable Power Systems. By Joseph Abdou
  11. Preemptive Investment Game with Alternative Projects By Michi Nishihara
  12. Decision Making in Uncertain and Changing Environments By Karl H. Schlag; Andriy Zapechelnyuk
  13. The Refined Best-Response Correspondence and Backward Induction By Dieter Balkenborg; Josef Hofbauer; Christoph Kuzmics

  1. By: Heller, Yuval
    Abstract: We prove that every undiscounted multi-player stopping game in discrete time admits an approximate correlated equilibrium. Moreover, the equilibrium has five appealing properties: (1) “Trembling-hand” perfectness - players do not use non-credible threats; (2) Normal-form correlation - communication is required only before the game starts; (3) Uniformness - it is an approximate equilibrium in any long enough finite-horizon 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
  2. 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
  3. By: Srihari Govindan; Robert Wilson
    Date: 2009–05–31
  4. By: Jung, Hanjoon Michael
    Abstract: We propose a complete version of the sequential equilibrium (CSE) and its alternative solution concept (WCSE) for general finite-period 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; Finite-period game; Solution Concept; Sequential Convergency; Sequential Equilibrium.
    JEL: C72
    Date: 2009–05–26
  5. 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 zero-sum 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
  6. 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
  7. 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 best-response 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
  8. 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 zero-sum 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 n-step 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
  9. 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
  10. 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
  11. 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 project-specific uncertainty. The proposed method enables us to evaluate the value of potential alternatives. The results not only extend previous studies with a one-dimensional 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
  12. By: Karl H. Schlag; Andriy Zapechelnyuk
    Date: 2009–06–08
  13. By: Dieter Balkenborg; Josef Hofbauer; Christoph Kuzmics
    Date: 2009–06–08

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