Rationalizable foresight dynamics

Abstract This paper proposes and studies the rationalizable foresight dynamics. A normal form game is repeatedly played in a random matching fashion by a continuum of agents who make decisions at stochastic points in time. A rationalizable foresight path is a feasible path of action distribution along which each agent takes an action that maximizes his expected discounted payoff against another path which is in turn a rationalizable foresight path. We consider a set-valued stability concept under this dynamics and compare it with the corresponding concept under the perfect foresight dynamics.

[1]  Kiminori Matsuyama,et al.  Increasing Returns, Industrialization, and Indeterminacy of Equilibrium , 1991 .

[2]  Kiminori Matsuyama,et al.  The market size, entrepreneurship, and the big push , 1992 .

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

[4]  K. Burdzy,et al.  Fast Equilibrium Selection by Rational Players Living in a Changing World , 2001 .

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

[6]  Drew Fudenberg,et al.  Learning in Games , 1998 .

[7]  I. Gilboa,et al.  A Model of Random Matching , 1992 .

[8]  Jörgen W. Weibull,et al.  Evolutionary Game Theory , 1996 .

[9]  Mitsuhiro Kaneda,et al.  Industrialization under Perfect Foresight: A World Economy with a Continuum of Countries , 1995 .

[10]  I. Gilboa,et al.  Social Stability and Equilibrium , 1991 .

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

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

[13]  K. Judd.  The law of large numbers with a continuum of IID random variables , 1985 .

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

[15]  Pierpaolo Battigalli,et al.  On Rationalizability in Extensive Games , 1997 .

[16]  Carlos Alós Ferrer.  Dynamical systems with a continuum of randomly matched agents , 1998 .

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

[18]  Mark Feldman,et al.  An expository note on individual risk without aggregate uncertainty , 1985 .

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

[20]  Akihiko Matsui,et al.  Best response dynamics and socially stable strategies , 1992 .

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

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

[23]  Paul Krugman,et al.  History versus Expectations , 1991 .

[24]  Richard T. Boylan.  Laws of large numbers for dynamical systems with randomly matched individuals , 1992 .