Bargaining, reputation and competition

This paper addresses the question of whether “playing the tough bargainer” is a useful strategy for rational negotiators in competitive environments. The unique equilibrium outcome of a continuous-time multilateral bargaining game between a single seller and two buyers (i.e., a three-player war of attrition game) show that it does not benefit the buyers—the long side of the market—if the probability of obstinacy is constant and independent of the initial demands. This result is robust in the sense that the buyers’ heterogeneity about their flexibility does not weaken the intensity of the competition. When the seller decides which buyer to negotiate first, he not only chooses his bargaining partner but also picks his outside option. The seller can strengthen his bargaining position against both buyers by picking the unattractive buyer, who is greedier or tougher than the other buyer, first and by leaving the attractive buyer aside because he starts the sequel with a strong outside option.