Some rationalizability results for dynamic games

We study the relation between dynamical systems describing the equilibrium behavior in dynamic games and those resulting from (single-player) dynamic optimization problems. More specifically, we derive conditions under which the dynamics generated by a model in one of these two classes can be rationalized by a model from the other class. We study this question under different assumptions about which fundamentals (e.g. technology, utility functions and time-preference) should be preserved by the rationalization. One interesting result is that rationalizing the equilibrium dynamics of a symmetric dynamic game by a dynamic optimization problem that preserves the technology and the utility function requires a higher degree of impatience compared to that of the players in the game.