An Investigation of the Effect of Free-Players on Global Cooperative Behavior in a Spatial Prisoner’s Dilemma Game Environment

Abstract

In this research, we introduced the concept of Free-Player who rejects to play the dictated rational strategy Defect of the original Prisoner’s Dilemma game setup. Then, we investigated whether Free-Players have any impact on the persistent and stable cooperative behavior of the Players in the context of two dimensional spatial Prisoner’s Dilemma game environment. In simulations, two different Player strategy update setups are considered: State-based Majority and Payoff-driven Stochastic. The results for both setups showed that Free-Players have impact on global cooperative behavior of the system. According to the obtained State-based Majority setup results, the increased number of Free-Players has no direct regulative impact on the control of global cooperative behavior of the proposed system. For the Payoff-driven Stochastic strategy update setup, the increased number of Free-Players has an observable regulative impact on the control of global cooperative behavior of the proposed system. However, the net effect of Free-Players on the cooperativeness of the environment was only in the range 0.007 < Net_Coop(α, β) < 0.036 while the attained cooperation ratio results are mostly not sensitive to the initial cooperation ratios. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.