Repeated Games with Recursive Utility:Cournot Duopoly under Gain/Loss Asymmetry

We study the repeated Cournot duopoly with recursive utility where the players discount gains more than losses. First, as in the standard model of discounted utility, we confirm that the optimal punishment equilibrium has a stick-and-carrot structure. Next, we explore its exact form in relation to the role of the asymmetry in discounting. We find that the discount factor used to evaluate losses controls the deterrence of a given punishment, while the discount factor used to evaluate gains influences the enforceability of the penalty. An increase in one of the two discount factors increases the most collusive equilibrium profit unless full collusion is already sustainable. However, the key to collusion is the loss discount factor: regardless of the level of the gain discount factor, full cooperation can be achieved if the loss discount factor is sufficiently high.