Wars of attrition with spending constraints

Abstract

We study wars of attrition with spending constraints. Specifically, there are two players with different values of the prize and costs of continuing wars, and they are endowed with limited budgets that can be used during the war. Two players compete by choosing the time at which they intend to give up within the constraints. We find the constrained mixed strategy equilibrium for this model and provide a full characterization of equilibrium depending on whether each player's constraint is binding or nonbinding.