Random Extensive Form Game and its Application to Bargaining

Abstract: We consider two-player random extensive form games where the payoffs at the leaves are drawn uniformly at random from a given feasible set C. We study the asymptotic distribution of the subgame perfect equilibrium outcome for binary-trees with increasing depth in various random 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 to two-player bargaining problems with a solid strategic justification.