Correlated and Mixed Nash Equilibrium

Project Overview #

Implemented algorithms to compute Correlated Nash Equilibria (CNE) and Mixed Nash Equilibria (MNE) for strategic games. The project applies optimization and game-theoretic techniques to analyze rational decision-making and equilibrium strategies in multi-agent environments.

Key Features #

• Mixed Nash Equilibrium: Computed mixed strategy equilibria for two-player strategic games.
• Correlated Equilibrium: Implemented algorithms to determine correlated equilibria using optimization techniques.
• Game Analysis: Evaluated player utilities, strategy distributions, and equilibrium stability.
• Strategy Visualization: Visualized payoff matrices and equilibrium outcomes for comparative analysis.
• Performance Evaluation: Tested algorithms across multiple game scenarios and benchmark examples.

Technologies Used #

• Python: Core implementation language.
• Game Theory: Mixed and Correlated Nash Equilibria.
• Linear Programming: Optimization for correlated equilibrium computation.
• NumPy: Numerical computation and matrix operations.
• Matplotlib: Visualization of strategies and payoff analysis.

Software Architecture #

• Game Engine: Represented normal-form games and payoff matrices.
• Equilibrium Solver: Implemented algorithms for Mixed and Correlated Nash Equilibrium computation.
• Optimization Module: Solved linear programming formulations for correlated equilibria.
• Analysis Module: Compared equilibrium solutions and evaluated player payoffs.
• Visualization Module: Generated graphical representations of strategies and results.

Impact and Applications #

• Game Theory Research: Demonstrates practical implementation of equilibrium computation algorithms.
• Multi-Agent Systems: Applicable to AI agents and strategic decision-making problems.
• Economic Modeling: Useful for analyzing competitive and cooperative interactions.
• Algorithm Design: Showcases optimization techniques for solving complex strategic games.