Evolutionary dynamics of group cooperation with asymmetrical environmental feedback

¹ School of Physics, Nankai University - Tianjin, 300071, China
² LMIB, NLSDE, BDBC and School of Mathematical Sciences, Beihang University - Beijing 100191, China
³ Department of Mathematics, Dartmouth College - Hanover, NH 03755, USA
⁴ Department of Biomedical Data Science, Geisel School of Medicine at Dartmouth Lebanon, NH 03756, USA

^(a) Xin.Wang-2@dartmouth.edu
^(b) feng.fu@dartmouth.edu

Received: 24 April 2019
Accepted: 24 May 2019

Abstract

In recent years, there has been growing interest in studying evolutionary games with environmental feedback. Previous studies exclusively focus on two-player games. However, extension to multi-player game is needed to study problems such as microbial cooperation and crowdsourcing collaborations. Here, we study coevolutionary public goods games where strategies coevolve with the multiplication factors of group cooperation. Asymmetry can arise in such environmental feedback, where games organized by focal cooperators may have a different efficiency than the ones by defectors. Our analysis shows that coevolutionary dynamics with asymmetrical environmental feedback can yield oscillatory convergence to persistent cooperation, if the relative changing speed of cooperators' multiplication factor is above a certain threshold. Our work provides useful insights into sustaining group cooperation in a changing world.