Rational Escalation

In many conflicts, protagonists commit resources that will not be returned. These situations, which often lead to apparently wasteful escalation, are well captured by the following "all-pay" auction. Two bidders bid repeatedly for a prize until one drops out. As usual the prize goes to the highest bidder but both bidders, the winner and the looser, pay their bids. Not only a process of escalation may be rational but it may be the only reasonable rational issue. We indeed prove that, if there is some uncertainty about the strength of the players, the only stable equilibrium may entail escalation. This result corroborates the idea that escalation is primarily a struggle to determine which player is the strongest one