Endogeneity of Alternating Offers in a Bargaining Game

We investigate an infinite horizon two-person simultaneous move bargaining game with incomplete information and discounted payoffs. The game takes the form of a concession game: in each period, each player chooses to give in or hold out. The game continues until at least one of the players chooses to give in, at which point agreement has been reached and the game terminates. For any discount factor, if the players' priors about each other's type are sufficiently asymmetric, there is a unique Nash equilibrium in which the two players alternate in their willingness to give in