Perseverance, Information and Stochastically Stable Outcomes

One bargainer from a finite population X, is matched at random with a bargainer from another finite population Y. They simultaneously precommit to "minimal" shares of a unit surplus. Populations differ in their degree of \underline{perseverance}, parameterized by $\lambda \in (0,1)$. If the players precommit to $x$ and $y$ such that $x+y\leq 1$, then player $i$ gets his demand $x_i$ as well as a fraction $\lambda_i$ of the unbargained surplus $(1-x-y)$. If $x+y>1$, they get nothing. When players play adaptively and sometimes make 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 $(1-\lambda_x)$ and $(1-\lambda_y)$. The surprise here is that the population that seemingly does well in the one shot encounters loses in the long run.