Nash equilibrium realization of population games based on social learning processes

Area of Science:

• Game Theory
• Computational Intelligence
• Artificial Intelligence

Background:

• Traditional game theory models often assume rational players, neglecting learning and adaptation.
• Simulating complex learning behaviors in multi-agent systems is a significant challenge.

Purpose of the Study:

• To develop a novel swarm intelligence algorithm for simulating imitative learning in two-population games.
• To analyze the convergence properties of this algorithm in games with different Nash equilibrium types.
• To compare the algorithm's performance against existing methods for mixed-strategy Nash equilibrium realization.

Main Methods:

• A new swarm intelligence algorithm is proposed, integrating particle swarm optimization (PSO) where players are treated as particles.
• Simulations were conducted on three distinct game types: Prisoner's Dilemma, Coin-Flip Game, and Coordination Game.
• The algorithm's convergence behavior was analyzed concerning pure-strategy and mixed-strategy Nash equilibria.

Main Results:

• The algorithm successfully converges to pure-strategy Nash equilibria when they exist.
• For games lacking pure-strategy Nash equilibria, the algorithm demonstrates periodic convergence to the unique mixed-strategy Nash equilibrium.
• The magnitude of periodic convergence is inversely proportional to the introspection rate.
• The proposed algorithm shows superior performance in achieving mixed-strategy Nash equilibrium compared to the Meta Equilibrium Q-learning algorithm.

Conclusions:

• The developed swarm intelligence algorithm effectively models imitative learning in game theory.
• It robustly converges to different types of Nash equilibria, showcasing its versatility.
• The algorithm offers an improved approach for finding mixed-strategy Nash equilibria in computational game theory.