Bilateral bargaining with endogenous status quo

Abstract

We consider a non-cooperative bargaining game where in each round, if a proposal is rejected, with a probability, the allocation implemented in the previous round is implemented as a status quo and the game proceeds to the next round, and with the complementary probability, no allocations are implemented and the negotiations break down. We show that there exists a unique stationary subgame perfect equilibrium such that in any round, a proposer offers a proposal such that the responder is indifferent between accepting and rejecting it and an agreement is achieved. If the probability of breakdown is close to zero, the sequence of equilibrium allocations evolves from the initial status quo to an allocation near the equilibrium allocation of the Rubinstein bargaining game over time. The effect of the initial status quo on the equilibrium allocations vanishes over time.