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Fearon (1994) - Rationalist Explanations For War (view source)
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|Has article title=Rationalist Explanations For War
|Has author=Fearon
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*This page is referenced in [[BPP Field Exam Papers]]
To address the puzzle of war it is important to consider both '''ex-ante''' and '''ex-post''' efficiency. If war is costly then it must be ex-post inefficient; the same final outcome could have occured without the conflict and the costs (or lesser costs). This is true even if there are benefits, unless fighting is a consumption good.
==Bargaining Preferred to War==
There existsa negotiated settlement that is pareto optimal:
:<math>u_A(x) > p- c_A\,</math>
For example in the risk neutral case <math>u_A(x) = x\,</math> and <math>u_B(1-x) = 1-x\,</math>, <math>x > (p - c_A)\,</math> and <math>x < (p +c_B)\,</math> solves this set of equations therefore:
<math>x \in (p - c_A, p +c_B)\,</math> is strictly preferred to fighting. Risk aversion will increase the range. This range exists because bargaining is ex-post inefficient. Proof: Choose an <math>\epsilon</math> such that <math>0<\epsilon<\min\{c_{A},c_{B}\}</math>. Let <math>a=\max\{0,p-\epsilon\}</math>, <math>b=\min\{p+\epsilon,1\}</math>. Consider <math>x'\in[a,b]</math> by weak concavity, <math>u_{A}(x')\geq x'</math>. Further <math>x'>p-c_{A}</math>, so it is better than war, because <math>x'\geq a \geq p-\epsilon \geq p- c_{A}</math>. Can make same argument for B.
#The leaders are risk neutral or risk averse. This is a reasonable assumption: A risk-acceptant leader is analogous to a compulsive gambler, that has the expected outcome of eliminating both the state and the regime.
#A continous range of settlement exists, to allow for feasible outcomes that lie in the range. But even without this, continuous side-payments would offer a solution, or randomization/alternation (c.f time-sharing!) would allow for negotiated outcomes. Though sharing a throne might be problematic.
==Private Information and Incentives to Misrepresent==
*Without private information, state <math>A\,</math> chooses to push state <math>B\,</math> back to its reservation level <math>p+c_B\,</math> and <math>B\,</math> acquiesces.
*With private information about either <math>p\,</math> or <math>c_B\,</math> state <math>A\,</math> faces a trade-off: the more territory it grabs the more likely the war.
*In equilibrium state <math>A \,</math> makes the trade-off and runs a positive risk of war.
But why could state <math>A\,</math> not simply have asked state <math>B\,</math> for the information as so avoided the (inefficient) war? Because there are strategic reasons to misrepresent!
If <math>A\,</math> gives <math>B\,</math> everything (i.e. sets <math>x_1=0\,</math>) this gives <math>B\,</math> thier largest possible payoff:
:<math>1 + \delta \frac{1-x_2}{1-\delta}\,</math>
Essentially, if <math>B\,</math>'s expected decline is too large relative to its costs of war, then <math>A\,</math>'s inability to commit makes preemptive war rational for <math>B\,</math>. Note also that if <math>B\,</math> could commit to fight in the second period, then <math>B\,</math>'s bargaining power would not fall, and preemptive war would be unnecessary. Furthermore, there is no private information here. This model, taken literally, suggests that rising powers should transfer away their military strength to prevent preemptive war against themselves.
===Strategic Territory===
One the topic of preemptive attacks, or of concessions, it is important to note that not all territory is, in the real world, created equal. Some territory may confer an advantage on the holder, and so it may be worth attacking to hold it (endogenously changing the probability of winning), or refusing to concede it (because the opponent may then be unable to commit to not attacking further).
