Since 2014, the United States, the EU and a number of other Western countries have been pursuing a policy of sanctions against Russia, which implies a set of financial, trade, economic, visa and other restrictions imposed on the activities of certain industries and sectors of the national economy, against individuals and companies in Russia, as well as their partners and counterparties abroad. To model the strategy of Russia in response to the sanctions, the methods of game theory are analyzed. This paper summarizes the main approaches of related game-theoretic models. Some varieties of classical games are used to analyze conflicts, conditions for changing the behavior of the target country, strategic interaction between institutions, the behavior of the population of the initiator countries and target countries. The areas of modeling multi-way games are the threat of using economic sanctions, evaluating the effectiveness of sanctions and determining the end of sanctions. We conclude that more dynamic approach to model the sanctions process, which could explain not only the result of sanctions actions, but also the evolution of strategic decisions taken by countries during sanctions activities and negotiations. Strategic games, the theory of moves and the adaptation of the Stackelberg oligopoly model are suggested as relevant analytical tools. As an example, a strategic game in a general form with a dynamic change of payment functions is proposed.