Exploring Nash Equilibrium: Foundations and Applications in Game Theory

Introduction

Game theory is a mathematical framework for analyzing strategic interactions among rational decision-makers. One of its most pivotal concepts is the Nash Equilibrium, introduced by John Nash in 1950. This report aims to explore the foundations of Nash Equilibrium, its significance in the realm of game theory, and its applications across various fields such as economics, political science, and biology. By delving into the theoretical underpinnings and real-world implications of Nash Equilibrium, this paper seeks to highlight its importance as both a conceptual tool and a practical framework for understanding competitive behavior.

Foundations of Nash Equilibrium

At its core, a Nash Equilibrium occurs in a game when each player’s strategy is optimal given the strategies of all other players. In this scenario, no player has anything to gain by unilaterally changing their strategy. This definition stems from the concept of mutual best responses, where each player