Ambiguity and long-run cooperation

Abstract

This paper studies the effects of ambiguity on long-run cooperation, by analyzing the infinitely repeated Prisoner’s Dilemma and its application to Cournot’s duopoly model. We show that ambiguity decreases the likelihood of cooperation in the infinitely repeated Prisoner’s Dilemma, regardless the level of optimism. In the economic application, we find that ambiguity is positively related with static equilibrium quantities and negatively related with the probability of sustaining a tacit collusion, i.e. positively related with competition. In fact, the critical discount factor associated with the probability of achieving a collusive equilibrium can be even higher than one for some parametric combinations. Nevertheless, depending on the level of optimism, a discontinuity can arise when ambiguity is too high, emerging a situation where collusion can be implemented as a short-run equilibrium. That is due to the fact that, for some parametric combinations, the economic application stops being a particular case of the Prisoner’s Dilemma and start behaving as different games in which cooperation can be achieved as a short-run pure Nash equilibrium. Finally, an alternative interpretation suggests an equivalence result: a Cournot’s duopoly with high ambiguity and relatively pessimist players behaves as a coordination game with exogenous payoffs