A typology of military conflict based on the Hirshleifer contest

In a canonical model of military conflict, victory and defeat depend stochastically on the difference of resources deployed by the conflict parties. The present paper offers a comprehensive analysis of that model. The unique Nash equilibrium reflects either (i) peace, (ii) submission, (iii) insurgency, or (iv) war. Intuitive predictions regarding possible transitions between these types of equilibria are obtained. The analysis identifies advances in weaponry as an important driver of conflict and, less often so, of its resolution. The formal derivation exploits the variation-diminishing property of higher-order Pólya frequency functions.