Finding the Stable Point of Game: A Quick Solution to Nash Equilibrium

Abstract

This essay will focus on the efficient solution of Nash Equilibrium and the analysis of strategies’ stability, aiming to provide completely information static games with a systematic and efficient framework for solving Nash Equilibrium and a risk assessment method. Traditional game theory models rely on the assumption of complete rationality and the its solution process is quite complex. During the real time application, there might be some challenges. The “fast solution method” processed in this essay simplifies the complex process through two-step procedure: First, apply line-drawing method to efficiently recognise the pure strategy Nash Equilibrium. If none exists, establish an equation based “Indifference Principle”. This method not only locates the stable state of the game, but also establishes a complete evaluation system from deterministic payoff to probabilistic risks through the analysis of “optimal response”, revealing the potential benefits and inherent risks of strategies. To further verify the effectiveness and explanatory power of the method, this essay simulates the example of Gomoku Game with the opposing styles of “aggressive vs conservative”. This research provides a rapid solution path for Nash equilibrium from a methodological perspective and deepens the understanding of strategy interaction, risk trade-offs, and the convergence process of equilibrium through case simulation in practical applications, which has reference value for the application of game theory in teaching, analysis, and strategy formulation.