Much of modern political science of conflict consists of testing game-theoretic models against evidence... either of the APSR or AJPS has dozens of such articles over the last decade. I actually wrote a thesis on game-theoretic models of war, so I have references if you'd like them.

Either way, we don't even have to conceptualize this as game theory (though explicit use of game theory may have prevented nuclear war--see Schelling's The Strategy of Conflict and his Nobel citation). Empires appear to frequently fight as a demonstration of their strength, if nothing else. Might that be why "giving in" to the Romans was followed by peace: other tribes could see that future wars would be met not by complacency but with force?