Generalized Potentials and Robust Sets of Equilibria

This paper introduces generalized potential functions of complete information games and studies the robustness of sets of equilibria to incomplete information. A set of equilibria of a complete information game is robust if every incomplete information game where payoffs are almost always given by the complete information game has an equilibrium which generates behavior close to some equilibrium in the set. This paper provides sufficient conditions for the robustness of sets of equilibria in terms of argmax sets of generalized potential functions and shows that the sufficient conditions generalize the existing sufficient conditions for the robustness of equilibria.

[1]  Takashi Ui,et al.  Robust Equilibria of Potential Games , 2001 .

[2]  N. Kukushkin.  Potential games: a purely ordinal approach , 1999 .

[3]  S. Hart,et al.  Potential, value, and consistency , 1989 .

[4]  R. Rosenthal.  A class of games possessing pure-strategy Nash equilibria , 1973 .

[5]  A. Rubinstein.  The Electronic Mail Game: Strategic Behavior Under "Almost Common Knowledge" , 1989 .

[6]  Glenn Ellison.  Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution , 2000 .

[7]  Stephen Morris,et al.  Correction to: Refinements and higher-order beliefs: a unified survey , 1997, The Japanese Economic Review.

[8]  Daisuke Oyama.  p-Dominance and Equilibrium Selection under Perfect Foresight Dynamics , 2002, J. Econ. Theory.

[9]  V. Strassen,et al.  Me\fehler und Information , 1964 .

[10]  William H. Sandholm,et al.  Almost global convergence to p-dominant equilibrium , 2001, Int. J. Game Theory.

[11]  Takashi Ui,et al.  A Shapley Value Representation of Potential Games , 2000, Games Econ. Behav..

[12]  Toshimasa Maruta,et al.  On the Relationship Between Risk-Dominance and Stochastic Stability , 1997 .

[13]  R. Selten.  Reexamination of the perfectness concept for equilibrium points in extensive games , 1975, Classics in Game Theory.

[14]  J. Mertens,et al.  ON THE STRATEGIC STABILITY OF EQUILIBRIA , 1986 .

[15]  Josef Hofbauer,et al.  A differential Game Approach to Evolutionary Equilibrium Selection , 2002, IGTR.

[16]  Akira Okada,et al.  On stability of perfect equilibrium points , 1981 .

[17]  Stephen Morris,et al.  Best Response Equivalence , 2002, Games Econ. Behav..

[18]  Stephen Morris,et al.  P-dominance and belief potential , 2010 .

[19]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[20]  Stephen Morris,et al.  Equilibrium Selection in Global Games with Strategic Complementarities , 2001, J. Econ. Theory.

[21]  L. Shapley,et al.  Potential Games , 1994 .

[22]  Kiminori Matsuyama,et al.  An Approach to Equilibrium Selection , 1995 .

[23]  H. Pietrantonio.  URBAN TRAVEL DEMAND MODELING: FROM INDIVIDUAL CHOICES TO GENERAL EQUILIBRIUM , 1997 .

[24]  Andrea Giovagnoni,et al.  The Electronic Mail , 1999 .

[25]  Mark Voorneveld,et al.  Best-response potential games , 2000 .

[26]  L. Blume.  The Statistical Mechanics of Strategic Interaction , 1993 .

[27]  Josef Hofbauer,et al.  Perfect Foresight and Equilibrium Selection in Symmetric Potential Games , 1998 .

[28]  H. Carlsson,et al.  Global Games and Equilibrium Selection , 1993 .

[29]  Satoru Takahashi,et al.  Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics , 2003 .

[30]  L. Shapley,et al.  REGULAR ARTICLEPotential Games , 1996 .

[31]  S. Morris,et al.  The Robustness of Equilibria to Incomplete Information , 1997 .

[32]  R. Tyrrell Rockafellar,et al.  Convex Analysis , 1970, Princeton Landmarks in Mathematics and Physics.

[33]  W. Arthur,et al.  The Economy as an Evolving Complex System II , 1988 .

[34]  L. Blume,et al.  POPULATION GAMES , 1995 .