Mixed nash equilibrium and its application in two-player zero-Sum games

Abstract

The Colonel Blotto game represents a classic case in game theory, embodying the essence of two-player zero-sum games. A vital game theory theorem has demonstrated a mixed Nash equilibrium in all zero-sum games. In this paper, the author will start with this classic game to expound the principles of mixed Nash equilibrium. Furthermore, the paper will explore the practical applications of mixed Nash equilibrium in the context of two-player zero-sum games, illustrating its significance in addressing real-world issues and decision-making. By delving into the Colonel Blotto game and its associated theories, the paper will reveal the importance and broad applicability of mixed Nash equilibrium, showcasing its role in various real-world applications, including competitive strategies, resource allocation, risk management, and more. This research will assist readers in gaining a better understanding of the concept of mixed Nash equilibrium and how to apply it to the resolution of practical problems.