Nash equilibrium realization of population games based on social learning processes

In the two-population game model, we assume the players have certain imitative learning abilities. To simulate the learning process of the game players, we propose a new swarm intelligence algorithm by combining the particle swarm optimization algorithm, where each player can be considered a particle. We conduct simulations for three typical games: the prisoner's dilemma game (with only one pure-strategy Nash equilibrium), the coin-flip game (with only one fully-mixed Nash equilibrium), and the coordination game (with two pure-strategy Nash equilibria and one fully-mixed Nash equilibrium). The results show that when the game has a pure strategy Nash equilibrium, the algorithm converges to that equilibrium. However, if the game does not have a pure strategy Nash equilibrium, it exhibits periodic convergence to the only mixed-strategy Nash equilibrium. Furthermore, the magnitude of the periodical convergence is inversely proportional to the introspection rate. After conducting experiments, our algorithm outperforms the Meta Equilibrium Q-learning algorithm in realizing mixed-strategy Nash equilibrium.