A punishment mechanism in the spatial public goods game with continuous strategies

¹ Department of Physics, Fuzhou University - Fuzhou, 350108, China
² College of Mathematics and Computer Science, Fuzhou, University - Fuzhou, 350108, China
³ Fujian Key Laboratory of Data Science and Statistics, Minnan Normal University - Zhangzhou, 363000, China

^(a) hxyang01@gmail.com
^(b) sinceway@fzu.edu.cn

Received: 25 August 2020
Accepted: 9 September 2020

Abstract

We propose a punishment mechanism in the spatial public goods game with continuous strategies. The value of strategy denotes the amount that an individual contributes to each group. In a group, the ones who contribute the least will be punished by others and punishers equally share the associated costs. It is found that the punishment fine and the number of individuals being punished in a group play important roles in the evolution of cooperation. Compared with the case of no punishment, the cooperation level increases (decreases) when the number of individuals being punished is less (more) than half of the total number of individuals in a group. For a fixed value of the enhancement factor, the cooperation level increases (decreases) as the punishment fine increases when individuals being punished are the minority (majority) in a group.