Equilibrium analysis of dynamic models of imperfect competition

Motivated by recent developments in applied dynamic analysis, this paper presents new sufficient conditions for the existence of Markov perfect equilibrium in dynamic stochastic games. The main results imply the existence of Markov perfect equilibrium provided the sets of actions are compact, the set of states is countable, the period payoff functions are upper semi continuous on the action profiles and lower semi continuous on actions taken by rival firms, and the transition function depends continuously on the actions. Additionally, if for each firm a static best reply set is convex, then the equilibrium can be taken to be in pure strategies. Sufficient conditions for the convexity of the best replies are presented and discussed. In particular, we introduce new sufficient conditions ensuring the dynamic programming problem each firm faces has a convex solution set and deduce the existence of Markov perfect equilibrium for this class of games. Our results expand and unify the available modeling alternatives and apply to several models of interest in industrial organization, including models of industry dynamics. JEL classification numbers: C73, C61, C62.