Ambiguity and Long-Run Cooperation in Strategic Games

This paper studies the effects of ambiguity on long-run cooperation in infinitely repeated games with strategic players. Using a neo-additive capacities framework, which allows us to work with a utility function that parametrically captures the degree of ambiguity, we determine a critical condition under which players can cooperate in equilibrium. Then, this result is applied to canonical problems of strategic interaction and potential cooperation: the Prisoner’s Dilemma and the Cournot and Bertrand duopoly models. The application leads to two main conclusions. First, ambiguity may alter the game structure to schemes where seeking conditions to sustain long-run cooperative agreements stops being desirable. In these cases, non-cooperation is more profitable in expected terms and is achievable as a short-run Nash equilibrium. This happens for parametric combinations usually characterized by large levels of ambiguity. Second, in cases where cooperation between individuals is still desirable, the critical discount factor needed to sustain the equilibrium can vary in very non-trivial ways with the ambiguity parameters. In some cases, games may not accept a feasible discount factor consistent with a cooperative equilibrium, even when the expected payoff of cooperating is larger.