Can the Nash Equilibrium Predict the Outcomes of Military Battles?

Abstract

Nash’s equilibrium is one of the most famous and widely used concepts of game theory. It has the ability to predict the best possible outcome based on the strategies of all the participating parties, thereby providing the most beneficial action for all of them to perform. It has been most valuable when applied to ideal conditions. For this reason, it has rarely been applied to war tactics which have real-world environments with varying conditions that rely heavily on the judgments of individuals. Here, we use case studies to test the success of the Nash equilibrium in predicting the outcome of military battles. Since this method is based on a static analysis, we are also interested in determining its accuracy when predicting the outcomes of battles where dynamics played a major role in the execution of the battle. In determining the possible outcomes, we consider the static factors of supplies, strengths, economic positions, and strategies of the combatants. Our results significantly extend the use of the Nash equilibrium into the “fog of war” and especially in exploring the capabilities of Nash equilibria in dealing with dynamic environments.