Spatial voluntary public goods games with tunable loners' payoff

¹ School of Statistics and Mathematics, Yunnan University of Finance and Economics - Kunming 650221, China
² Center for OPtical IMagery Analysis and Learning, Northwestern Polytechnical University - Xi'an, 710072, China
³ School of Mechanical Engineering, Northwestern Polytechnical University - Xi'an, 710072, China
⁴ School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance Shanghai, 201209, China

Received: 14 September 2019
Accepted: 28 October 2019

Abstract

Based on the spatial voluntary public goods games, we investigate how loners' income affects the evolution of cooperation on square lattice. In the voluntary model, loners can exit the game by holding a small fixed payoff. By introducing a tunable parameter, we make loners payoff positively related to the synergy factor r. Through Monte Carlo simulations, we found that a higher loners' income essentially weakens their own survivability, but strengthens the competitiveness of cooperators. Through the analysis of the evolution process, we clarify the reasons as to how low-income loners totally dominate the population. For other results, we have studied from the perspective of spatial distribution, and found that a higher loners' payoff leads to a more intense strategies transition during the loop dominance process. Further, the result of the strategies transition rate once again shows how the loner's income affects the evolution of cooperation.