An Evolutionary Game With the Game Transitions Based on the Markov Process

TL;DR

This paper introduces a model of evolutionary games with dynamic game transitions influenced by Markov processes, incorporating reputation mechanisms to analyze their effects on cooperation in populations.

Contribution

It presents a novel framework combining Markov-based game transitions and reputation effects to study cooperation evolution, extending traditional static models.

Findings

Transition rates significantly affect cooperation levels.

Reputation mechanisms enhance cooperative behavior.

Network size influences cooperation frequency.

Abstract

The psychology of the individual is continuously changing in nature, which has a significant influence on the evolutionary dynamics of populations. To study the influence of the continuously changing psychology of individuals on the behavior of populations, in this paper, we consider the game transitions of individuals in evolutionary processes to capture the changing psychology of individuals in reality, where the game that individuals will play shifts as time progresses and is related to the transition rates between different games. Besides, the individual's reputation is taken into account and utilized to choose a suitable neighbor for the strategy updating of the individual. Within this model, we investigate the statistical number of individuals staying in different game states and the expected number fits well with our theoretical results. Furthermore, we explore the impact of transition rates between different game states, payoff parameters, the reputation mechanism, and different time scales of strategy updates on cooperative behavior, and our findings demonstrate that both the transition rates and reputation mechanism have a remarkable influence on the evolution of cooperation. Additionally, we examine the relationship between network size and cooperation frequency, providing valuable insights into the robustness of the model.