Reputational Wars of Attrition with Complex Bargaining Postures

Consider a two-person intertemporal bargaining problem in which players choose actions and collect payo¤s while bargaining proceeds. Theory is silent regarding how the surplus is likely to be split, because a folk theorem applies. Perturbing such a game with a rich set of behavioral types for each player yields a speci…c asymptotic prediction for how the surplus will be divided, as the perturbation probabilities approach zero. Behavioral types may follow nonstationary strategies and respond to the opponent’s play. How much should a player try to get, and how should she behave while waiting for the resolution of bargaining? In both respects she should build her strategy around the advice given by the ’Nash bargaining with threats’ theory developed for two-stage games. The results suggest that there are forces at work in some dynamic games that favor certain payo¤s over all others. This is in stark contrast to the classic folk theorems, to the further folk theorems established for repeated games with two-sided reputational perturbations, and to the permissive results obtained in the literature on bargaining with payo¤s-as-you-go.