British naval commanders were somewhat rational in avoiding battles

Mutual optimism theory holds that mutually optimistic beliefs about outcomes cause international conflict. Because beliefs are unobservable, this theory is difficult to test systematically. Here, I present a clean test of theory that relies exclusively on observable variables by exploiting novel features of naval battles in the age of sail, most notably an admiral’s ability to avoid battle by simply sailing away. Using a formal model, I show that the outcome of mutual naval battles, where either side could avoid battle by sailing away, should not be predictable from observable capability indicators. The outcome of unilateral battles, where only one side could sail away to avoid fighting, should be predictable from these same indicators. I test these predictions against all squadron-level British naval battles from 1650 to 1833. I show that observable strength indicators are substantially less predictive in mutual battles, confirming the core key theoretical prediction.

That is from David Lindsey, via the excellent Kevin Lewis.  Aumann theorem for them!