Strategic Extremism: Bargaining with Endogenous Breakdown Probabilities and Order of Play

The purpose of this paper is to provide a simple example of an alternating offers bargaining model with breakdowns, in which both the breakdown probabilites and the order of play are determined endogenously. We consider two countries in a conflict over a contested asset. We assume that one of the countries can use extremism as a strategic tool in the conflict. Extremism is useful because it provides a credible threat. On the other hand, it involves a risk since it can cause damage, with probabilities that depend on the outcome of the game. We consider a three-stage game in which the use of extremism, the order of play and the division of the contested asset are determined in the three stages, respectively. We show that the game has unique subgame perfect equilibrium in which: extremism is indeed used strategically, the probability of a breakdown is strictly positive and, most importantly, the country that uses extremism moves first in the asset division bargaining stage. The order of play is determined endogenously in this model, because the expected size of the pie is affected by the order of play. Specifically, we show that the equilibrium order of play yields the largest expected pie size.