We construct a general equilibrium model of international trade where each government agent has a system of tariffs as his strategic variables. Our general equilibrium model follows recent contributions allowing incompleteness and intransitivity of consumer preferences. Government agents are assumed to have incomplete information on the preferences of domestic consumers and the availability of commodities. The behavior of each government agent is to choose a system of tariffs to maximize the estimated preferences of domestic consumers with a constraint on an estimated availability of commodities. We introduce an equilibrium concept so that (a) estimated preferences and an estimated available set of commodities are compatible with an observed state of the world economy and (b) a consumption bundle intended by each government agent coincides with a consumption bundle chosen by its domestic consumers. Our major goal is to provide the existence of such an equilibrium.