Perfect Sequential Equilibrium in Bargaining with Incomplete Information

I derive a refinement of sequential equilibria of a noncooperative bargaining game when one player has incomplete information about the time preference of the other player. I show that if the types for this latter player are drawn from some totally ordered and finite lattice, Grossman & Perry’s (1986) Perfect Sequential Equilibrium selects the mixture (by prior belief over types) of the subgame perfect equilibria corresponding to the extrema of the set of types that survive elimination in preceding stage games. Additionally, if best responses are monotone in type for both, a properness condition á la Myerson (1978) can be imposed on the relative probabilities of out-of-equilibrium moves to harness the idea of threatening opponents by incredible belief