All-pay war

We study a model of war in which the outcome is uncertain not because of luck on the battlefield (as in standard models), but because the involved countries lack information about their opponent. In our model their production and military technologies are common knowledge, but their resources are private information. Each country decides how to allocate its resources to production and warfare. The country with the stronger military wins and receives aggregate production. In equilibrium the country with a comparative advantage in warfare allocates all resources to warfare for low resource levels and follows a non-decreasing concave strategy thereafter. The opponent allocates a constant fraction of its resources to warfare for low resource levels and follows an increasing non-linear strategy thereafter. From an ex ante perspective the country with a comparative advantage in warfare is likely to win the war unless its military technology is much weaker than the opponent’s.