Abstract: The quantitative analysis of trading wars is now an actual and modern problem although the first works on optimisation of the custom duties date back to the end of the 19th century. The problem of reducing the number of possible solutions to the conflict and precise identifying of the optimal strategies is important. Applying mathematics makes the problem more formal, allows removing political tension in search of optimum solutions to all participants of the trading conflict. We consider that some state sells a product manufactured both in the country and abroad to other countries. The country-consumer of the product faces a choice of the import regulation in relation to the situation by means of the import duty size. A goal of such regulation may be the income of taxes and customs payments or the growth of the domestic manufacturer part in sales volumes. A goal of the importer which it achieves by the import volume variation is either profit, or a number of workplaces in the countries making the imported product. We introduce three multicriteria problems which correspond to different purposes of economic agents. The Pareto set is constructed for each problem. The main attention is paid to the Pareto set reducing based on additional information on the preference relation of the economic agents. Several calculations are made and illustrative examples are given. Keywords: quantitative analysis; optimal tariff; trade policy; risk management; multicriteria problem; Pareto set
