Rationalizable foresight dynamics

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.