In organizational and economic tasks related to decision-making at various levels of the hierarchy in various economic systems, conflict situations often arise. A distinctive feature of any conflict is that the interests of its parties are mutually opposed, that is, the economic result (winning) of one participant in the conflict is equal to the loss of the other participant. With the help of conflict situations, one can describe the opposition of competitors to each other in the oligopoly market, the struggle for resources between various interested parties, the relationship of tax authorities with unscrupulous taxpayers, and some other situations. The article discusses the practical application of the theory of antagonistic games to the problems of choosing effective solutions in the economy, analyzes the methodological features of this theory, formulates the main problems that arise when using antagonistic games in organizational and economic problems, analyzes some practical examples in which the use of this theory can be appropriate. Special attention is paid to the solution of computational problems, the economic interpretation of such game theory terms as strategy, win, efficiency criterion. As the main result of the work, it should be noted that: 1. Despite the fact that the theory of antagonistic games is currently developed mainly as a purely mathematical model, it may well find application in solving practical economic problems, in particular, for the oligopoly market. 2. Using the methods of the theory of antagonistic games to select optimal solutions in conflict situations encounters a number of difficulties, among which the most important are:
 determination of the set of strategies of the participants in the conflict;
 the correct choice of the criterion on the basis of which the conflict situation is analyzed;
 establishing the relationship between the optimality criterion and the strategies of the participants;
 formation of an efficiency matrix based on the values of this criterion for each combination of strategies of the participants in the conflict;
 search for equilibrium situations;
 study of the possibility of a multi-criteria choice in the context of a conflict of interest.
 
 The most widely used when choosing effective solutions in a conflict of interest is the principle of a guaranteed result, which is the easiest way to determine the equilibrium strategies of the participants.