Costly preparations in bargaining

Abstract

We model costly preparations in negotiations and study their effect on agreements in a bilateral bargaining game. In our model, players bargain over a unit pie, where each player needs to pay a fixed cost in the beginning of every period t, if he wants to stay in the game in period t+1 in case a deal has not been reached by the end of t. Whether a player has paid this cost (i.e., prepared for negotiations in t+1) is his private information. If only player i stops paying, then player j receives the entire pie. We characterize a “war of attrition” equilibrium, which is a symmetric equilibrium. We do not know whether the game has other symmetric equilibria, but we show that if such an equilibrium exists, its payoff converges to zero as the frictions (discounting and preparation cost) vanish. Efficiency can be obtained by asymmetric play. Specifically, with asymmetric strategies every Pareto‐efficient payoff vector can be approximated in equilibrium, provided that the cost of preparations is sufficiently small and that the discount factor is sufficiently close to one.