On the diffuseness of incomplete information game

We introduce the “relative diffuseness” assumption to characterize the differences between payoff-relevant and strategy-relevant diffuseness of information. Based on this assumption, the existence of pure strategy equilibria in games with incomplete information and general action spaces can be obtained. Moreover, we introduce a new notion of “undistinguishable purification” which strengthens the standard purification concept, and its existence follows from the relative diffuseness assumption.

[1]  Konrad Podczeck,et al.  On purification of measure-valued maps , 2009 .

[2]  Yeneng Sun Distributional Properties of Correspondences on Loeb Spaces , 1996 .

[3]  Yeneng Sun,et al.  The Necessity of Nowhere Equivalence , 2013, 1307.7168.

[4]  Yeneng Sun,et al.  Pure strategy equilibria in games with private and public information , 2007 .

[5]  Haifeng Fu Mixed-strategy equilibria and strong purification for games with private and public information , 2008 .

[6]  Jianwei Wang,et al.  Purification, saturation and the exact law of large numbers , 2012 .

[7]  H. Jerome Keisler,et al.  Model theory of stochastic processes , 2016 .

[8]  Yeneng Sun,et al.  The Dvoretzky-Wald-Wolfowitz theorem and purification in atomless finite-action games , 2006, Int. J. Game Theory.

[9]  Roy Radner,et al.  Private Information and Pure-Strategy Equilibria , 1982, Math. Oper. Res..

[10]  H. Jerome Keisler,et al.  Adapted probability distributions , 1984 .

[11]  M. A. Khan,et al.  On Sufficiently Diffused Information and Finite-Player Games with Private Information , 2012 .

[12]  Peter A. Loeb,et al.  Purification and saturation , 2009 .

[13]  C. Castaing,et al.  Convex analysis and measurable multifunctions , 1977 .

[14]  P. Reny,et al.  On the Existence of Monotone Pure Strategy Equilibria in Bayesian Games , 2009 .

[15]  J. Wolfowitz,et al.  Elimination of Randomization in Certain Statistical Decision Procedures and Zero-Sum Two-Person Games , 1951 .

[16]  Yeneng Sun,et al.  Purification of measure-valued maps , 2006 .

[17]  Susan Athey,et al.  Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information , 1997 .

[18]  M. Ali Khan,et al.  Non-cooperative games on hyperfinite Loeb spaces , 1999 .

[19]  John C. Harsanyi,et al.  Games with Incomplete Information Played by "Bayesian" Players, I-III: Part I. The Basic Model& , 2004, Manag. Sci..

[20]  H. Jerome Keisler,et al.  Why saturated probability spaces are necessary , 2009 .

[21]  M. Ali Khan,et al.  Pure strategies in games with private information , 1995 .

[22]  R. Weber,et al.  DISTRIBUTIONAL STRATEGIES FOR GAMES WITH INCOMPLETE INFORMATION * t , 2007 .

[23]  Aloisio Araujo,et al.  Pure Strategy Equilibria of Single and Double Auctions with Interdependent Values , 2006, Games Econ. Behav..

[24]  Erik J. Balder,et al.  Generalized Equilibrium Results for Games with Incomplete Information , 1988, Math. Oper. Res..

[25]  Kim C. Border,et al.  Infinite Dimensional Analysis: A Hitchhiker’s Guide , 1994 .

[26]  Robert J. Weber,et al.  Distributional Strategies for Games with Incomplete Information , 1985, Math. Oper. Res..

[27]  M. Ali Khan,et al.  On a private information game without pure strategy equilibria1 , 1999 .