Equilibria of Attacker-Defender Games

Attempts at predatory capture may provoke a defensive response that reduces the very value of the predated resource. We provide a game-theoretic analysis of simultaneous-move, two-player Attacker-Defender games that model such interactions. When initial endowments are equal, Attackers win about a third of such games in equilibrium. Under power disparities, Attackers become particularly aggressive when they are approximately one-third poorer than Defenders. With non-conflictual outside options Attackers become exceptionally aggressive when their opponent has access to high-benefit, low-cost production, and refrain from attack most when they are unilaterally provided with a high-benefit, high-cost production option.