Deciding on a reciprocal action with the help of game theory

A legal but unfriendly act of a country against another country in retaliation for an unfriendly but legal act and in order to force that country to change its unfriendly behavior is called "reciprocal action". The decision of the aggrieved government to choose the type of unilateral action is a challenging one, because its reciprocal action provokes the reaction of the responsible government and the international community. In this article, we model the decision-making situation with the help of zero-sum games. In fact, we correspond the conditions of reciprocal action of the injured government with the game model (X, Y, A) in which X is a set of possible reciprocal actions of the injured government (friend player) against the responsible government, Y is a set of possible reactions of the responsible government (enemy player) and A is the utility matrix of the injured government. We solve the model by Maximin method, in this regard we use the theory of game reduction to a linear programming problem and solve it in MATLAB software.