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)  or Cripps et al. (2005)  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.
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