Computing equilibria of dynamic games

This paper develops a numerical method for computing equilibria of dynamic games with state variables, and applies it to an oligopoly game with endogenous productive capacity. Our algorithm allows us to study the nature of cooperation and examine how the ability to collude is affected by state variables, such as current capacity. We study whether investment decisions increase the gains from cooperation, or present opportunities to deviate from collusive agreements and reduce the potential for cooperation. Our results indicate that there is rich set of equilibrium outcomes that had not been discovered due to restrictive assumptions made in earlier papers. These include asymmetric equilibria where market power fluctuates between firms and equilibria in which firms do strive for cooperation after a phase of uncooperative behavior that involves over investment and over production. The results indicate that restricting attention to symmetric Markov equilibria eliminates rich and interesting outcomes that shed light on the nature of collusion and cooperation, as the nature of cooperation evolves with the history of firm interaction and investment.