War's inefficiency puzzle
War's inefficiency puzzle is a research question asking why unitary-actor states would choose to fight wars when doing so is costly. James Fearon’s Rationalist Explanations for War and Robert Powell's In the Shadow of Power, which launched rational choice theory in international relations, provide three possible answers: private information and incentives to misrepresent, commitment problems, and issue indivisibility.
Fearon has three basic assumptions about war. First, war is a more costly choice than peace. Second, war is predictably unpredictable. In other words, although neither side may be sure exactly who will win, they can agree on the relatively likelihood each will win. And third, there are no direct benefits from fighting.
Thus, using John von Neumann and Oskar Morgenstern expected utility functions, Fearon finds the expected utility for war for states A and B, which are PA - CA and (1 - PA) - CB, where PA is A's probability of winning a war, CA is A's costs for war (proportional to how much they value the utility), and CB is B's costs for war (proportional to how much they value the utility). With simplification, if X is A's share of a peaceful settlement, Fearon finds that peace is better than war when PA - CA < X < PA + CB. A satisfactory X exist if PA + CB > PA - CA, or CA + CB > 0. Because CA and CB are individually greater than 0, so is their sum. Therefore, the inequality holds and so some settlement is mutually preferable to war.
The question is why two rational states cannot find an X that satisfies both sides, even though one must always exist and war is the worst feasible payoff for both sides.
One obvious reason is that each state simply believes it is more powerful than it really is. For example, two states that each believe they are infinitely powerful would have a difficult time bargaining with each other. War, then, can erupt with incomplete information regarding the distribution of power.
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