War and peace: a liberalist reassessment

In a simple formal model of two-country, two-good with an elementary Conflict Technology, we use rudimentary game theoretics to study the matter of war and peace where under peace, cooperative exchange takes place and where, in case of war, the winner takes all through appropriation of the whole endowment left after payment of armament expenditures. We provide conditions under which war is inevitable then go on to characterize situations where war, still probable, is not necessarily the final outcome. In this case, cooperative exchange is profitable for both countries, and they should take this welfare gain from trade into account in the determination of their armament expenditures. This problem will be cast in terms of a two-stage game, the final stage is modelled as a Nash Bargaining solution with endogenous threat-point, and the precedent stage, aimed at the determination of armament expenditure, is modelled as a Nash Bayesian Equilibrum in the context of incomplete information. With a simple rule of Bayesian inferences, it is possible to transform the game under incomplete information into one under imperfect information and solve for pure strategies. Using backward induction to yield the perfect equilibrium of this two-stage game, this paper provides a simple solution which concurs with the liberalist view, that economic gain in trade would enhance not war but peace between nations.