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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==

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:

*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.

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).