A game theory model of tariff rate quotas in international trade

In this paper, we consider several international companies with production facilities in different countries that aim to sell a homogeneous product to different demand markets in different countries. The importing countries set up a system of two-tiered tariff rate quotas: a lower tariff applies until the quantity of the product to be purchased is below a prescribed threshold, and an upper tariff applies once the threshold is exceeded. We assume that the threshold is a variable controlled by each importing country and that the upper tariff is a function of it. We propose a generalized Nash game model in which the exporting companies compete with each other and the importing countries. The game is investigated in the framework of variational inequalities and a monotonicity result is proved under mild assumptions. Finally, some preliminary numerical experiments illustrate the proposed model.