Clever agents in young's evolutionary bargaining model

In the models of Young (1993, Econometrica 61, 57-84; 1993, J. Econ. Theory 59, 145-168), boundedly rational individuals are recurrently matched to play a game, and they play myopic best replies to the recent: history of play. It could therefore be an advantage to instead play a myopic best reply to the myopic best reply, something boundedly rational players might conceivably also do. We investigate this possibility in the context of Young's (J. Econ. Theory 59, 145-168) bargaining model. It turns out that "cleverness" in this respect indeed does have an advantage in some cases. However, if all individuals are equally informed about past play, in a statistical sense, then the Nash bargaining solution remains the unique long-run outcome when the mutation rate goes to zero: Journal of Economic Literature Classification Numbers C70, C78.