Perseverance, Information and Stochastically Stable Outcomes

One bargainer from a nite population X, is matched at random with a bargainer from another nite population Y. They simultaneously precommit to "minimal" shares of a unit surplus. Populations di er in their degree of perseverance, parameterized by 2 (0; 1). If the players precommit to x and y such that x+ y 1, then player i gets his demand xi as well as a fraction i of the unbargained surplus (1 x y). If x+ y > 1, they get nothing. When players play adaptively and sometimesmake errors as in Young (1993b), in the long run, a single division of surplus is observed most often. This is close to the asymmetric Nash bargaining solution with the weights (1 x) and (1 y). The surprise here is that the population that seemingly does well in the one shot encounters loses in the long run.