Random Extensive Form Games and its Application to Bargaining

We consider two-player random extensive form games where the payoffs at the leaves are independently drawn uniformly at random from a given feasible set C. We study the asymptotic distribution of the subgame perfect equilibrium outcome for binarytrees with increasing depth in various random (or deterministic) assignments of players to nodes. We characterize the assignments under which the asymptotic distribution concentrates around a point. Our analysis provides a natural way to derive from the asymptotic distribution a novel solution concept for two-player bargaining problems with a solid strategic justification.