# 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.

## The puzzle

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.

## Information problems

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.

But Fearon points out that this is not a completely rational explanation for war. Recall that war is the worst payoff for both sides. Consequently, states actually have incentive to reveal how powerful they are to the other side, as to avert the costs of war. The problem with such information transmission is that states actually have incentive to overrepresent how powerful they are. Generally speaking, a state that is extremely powerful will receive a better settlement than an extremely weak one. Thus, a state has incentive to look powerful to try to coerce a good peaceful settlement even if it comes at the risk of falling into war. This prevents the states from credibly revealing how powerful they are to each other.

## Commitment problems

Fearon also finds that both states can prefer fighting with complete information when under situations with shifting power. There are two versions of this. First, when there are sufficiently great advantages for striking first, then neither side can credibly commit to any distribution of the stakes. (The cult of the offensive, an explanation for World War I, roughly makes this argument.) Second, if one side is slowly getting more powerful as a function of time, then the declining power may receive a better distribution of the stakes by fighting a preventive war now rather than having to accept a peaceful settlement later. (The rising power still has incentive to negotiate when it reaches its peak power because war is costly.)

## Issue indivisibility

Finally, each may gain from war when the stakes are not infinitely divisible. (For example, control over a holy city.) War will occur when both states' expected utilities are positive. However, Fearon largely discredits issue indivisibility as a rationalist explanation for war, claiming that states can link other issues or make side payments to eliminate the inefficiency. Additionally, the vast majority political goods (territory, money, control of a government) are divisible with sufficient creativity.

## Endogenous Destruction

In a series of two papers, Chang and Luo (2013, 2017) provide a possible explanation to the Puzzle. They show that the key to the puzzle lies in destruction. In the absence of destruction, or when destruction is constant or proportionate to remaining resources after war, war is more costly than peace as Fearon has assumed. However, when destruction is endogenous and increases with weapon allocation, the authors show that the two conflicting states allocate more weapons under settlement/negotiation. When destruction is small, it is shown that the expected utility from war is higher than peace.