Cumbersome coordination in repeated games

This paper examines the role communication between players might serve in enabling them to reach an agreement on the future play of a repeated game. The property of the communication process that we focus on is the amount of time it takes to complete. We characterize the effects of such communications processes indirectly by determining the set of agreements they may yield. A weak and a strong criterion are introduced to describe sets of agreements that are ‘stable’ in the sense that players would follow the current agreement and not seek to reach a new agreement. We show that as players become extremely patient, strongly stable sets converge to Pareto efficient singletons. We apply the stability criteria to Prisoner's Dilemmas and show how the unique strongly stable set reflects asymmetries in the players' stage-game payoffs. Finally, we model the communication process as a Rubinstein alternating-offer bargaining game and demonstrate that the resulting agreements help characterize the strongly stable set for a general class of communication mechanisms.