<p>This study presents a numerical approach for solving a min–max differential game with a Cauchy initial value problem (CIVP) as the state trajectory for the differential game. The finite difference method is utilized to compute the numerical solution, and a stability analysis is conducted. A comparison is made between the exact and numerical solutions to evaluate the accuracy of the method. Furthermore, the study investigates a min–max differential game modeling the spread of the coronavirus, described by a partial differential equation, with particular attention to the stability of its numerical solution. Illustrative examples are provided to demonstrate the effectiveness and reliability of the proposed approach. Based on numerical analysis, we found that the spread of the coronavirus tends to decrease as the area increases, and that a player’s participation decreases as their misbehavior increases.</p>