Evolutionary Stability in Alternating-Offers Bargaining Games

This paper characterizes modified evolutionarily stable strategies (messes) in Rubinstein's alternating-offers, infinite-horizon bargaining game. The mess concept modifies the idea of a neutrally stable strategy by favoring a simple strategy over a more complex strategy when both yield the same payoff. We show that if strategy A is a mess, then the use of A by both players is a Nash equilibriumin which an agreement is achieved immediately, and neither player would be willing to delay the agreement by one period in order to achieve the other player's share of the surplus. Each player's share of the surplus is then bounded between the shares received by the two players in the unique subgame-perfect equilibrium of Rubinstein's game. As the probability of a breakdown in negotiations becomes small (or discount factors become large), these bounds collapse on the subgame-perfect equilibrium. These results continue to hold when offers must be made in multiples of a smallest monetary unit.