p-Best response set

This paper introduces a notion of p-best response set (p-BR). We build on this notion in order to provide a new set-valued concept: the minimal p-best response set (p-MBR). After proving general existence results of the p-MBR, we show that it characterizes set-valued stability concepts in a dynamic with Poisson revision opportunities borrowed from Matsui and Matsuyama [An approach to equilibrium selection, J. Econ. Theory 65 (1995) 415-434.] Then, we study equilibrium selection. In particular, using our notion of p-BR, we generalize Morris et al. [p-Dominance and belief potential, Econometrica 63 (1995) 145-157.] that aimed to provide sufficient conditions under which a unique equilibrium is selected in the presence of higher order uncertainty.

[1]  Sjaak Hurkens.  Learning by Forgetful Players , 1995 .

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

[3]  Pierpaolo Battigalli,et al.  Rationalizable bidding in first-price auctions , 2003, Games Econ. Behav..

[4]  J. Weibull,et al.  Strategy subsets closed under rational behavior , 1991 .

[5]  David Pearce.  Rationalizable Strategic Behavior and the Problem of Perfection , 1984 .

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

[7]  E. Kalai,et al.  Persistent equilibria in strategic games , 1984 .

[8]  Fuhito Kojima.  Risk-dominance and perfect foresight dynamics in N-player games , 2006, J. Econ. Theory.

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

[10]  P. Reny.  On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games , 1999 .

[11]  Daisuke Oyama,et al.  Rationalizable Foresight Dynamics: Evolution and Rationalizability , 2002 .

[12]  H. Young,et al.  The Evolution of Conventions , 1993 .

[13]  J. Nash.  Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

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

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

[16]  Olivier Tercieux,et al.  p-Best response set and the robustness of equilibria to incomplete information , 2006, Games Econ. Behav..

[17]  R. Aumann,et al.  Epistemic Conditions for Nash Equilibrium , 1995 .

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

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

[20]  Daisuke Oyama,et al.  Rationalizable foresight dynamics , 2006, Games Econ. Behav..

[21]  B. Bernheim.  Rationalizable Strategic Behavior , 1984 .

[22]  Stephen Morris,et al.  Generalized Potentials and Robust Sets of Equilibria , 2003, J. Econ. Theory.

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

[24]  I. Glicksberg.  A FURTHER GENERALIZATION OF THE KAKUTANI FIXED POINT THEOREM, WITH APPLICATION TO NASH EQUILIBRIUM POINTS , 1952 .

[25]  D. Monderer,et al.  Approximating common knowledge with common beliefs , 1989 .