A differential game model of tariff war

We present a simple two(-country) by two(-good) differental game model of international trade in which the governments of the two countries play a tariff-setting game. We explicitly derive a unilateral optimum tarifff rate and then a Markov-perfect equilibrium pair of tariff strategies (bilateral optimum tariff strategies) and compare the welfare level of each country among autarchic, free-trade, unilateral and bilateral optimum-tariff equilibria.