Strategy Competition Dynamics of Multi-Agent Systems in the Framework of Evolutionary Game Theory

There is the recent boom in investigating the control of evolutionary games in multi-agent systems, where personal interests and collective interests often conflict. Using evolutionary game theory to study the behaviors of multi-agent systems yields an interdisciplinary topic which has received an increasing amount of attention. Findings in real-world multi-agent systems show that individuals have multiple choices, and this diversity shapes the emergence and transmission of strategy, disease, innovation, and opinion in various social populations. In this sense, the simplified theoretical models in previous studies need to be enriched, though the difficulty of theoretical analysis may increase correspondingly. Here, our objective is to theoretically establish a scenario of four strategies, including competition among the cooperatives, defection with probabilistic punishment, speculation insured by some policy, and loner. And the possible results of strategy evolution are analyzed in detail. Depending on the initial condition, the state converges either to a domination of cooperators, or to a rock-scissors-paper type heteroclinic cycle of three strategies.