A two-sided reputation result with long-run players

We establish reputation results, under two sided incomplete information, for a class of repeated games. We consider a repeated game that satisfies the assumptions of either Atakan and Ekmekci (2012) [3] or Cripps et al. (2005) [6] and we assume that both players are Stackelberg types with positive probability. If the stage game is not a common interest game, then equilibrium play converges to the unique equilibrium of a continuous time war of attrition as the stage game is repeated arbitrarily frequently. Alternatively, if the stage game is a common-interest game, then the playersʼ equilibrium payoffs converge to their highest payoffs as the stage game is repeated arbitrarily frequently.