Methodological aspects on solving zero-sum matrix games in pure and mixed strategies of size 2*2

In this paper the methodology for solving matrix games is presented, addressing two distinct types of situations: saddle-point games solved in pure strategies and 2×2 dimensional games solved using mixed strategies. In the first part, the conditions for the existence of the saddle point and the procedures for determining the optimal strategies in their case are analyzed. In the second part, graphical and analytical methods for solving 2×2 dimensional games are detailed when the saddle point is missing, with an emphasis on the use of mixed strategies to identify optimal solutions. The article provides both theoretical foundations and practical applications, contributing to a thorough understanding of zero-sum game theory.