Evolving wars of attrition

This paper models a war of attrition that evolves over time. Two players fight over a prize until one surrenders. The flow costs of fighting depend on a state variable that is public but changes stochastically as the war unfolds. In the unique equilibrium, each player surrenders when the state becomes adverse enough; for intermediate states, both players fight on. In an extension, the baseline model is augmented to allow for unilateral concessions of part of the prize. Such concessions can be beneficial if they disproportionately sap the opponent's incentive to fight. The evolving war of attrition with concessions yields predictions regarding delay and the eventual division of the prize that differ from conventional models of bargaining as well as reputational wars of attrition.