Ability-based evolution promotes cooperation in interdependent graphs

¹ School of Mechanical Engineering and Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University - Xi'an 710072, China
² School of Statistics and Mathematics, Yunnan University of Finance and Economics - Kunming, Yunnan 650221, China
³ School of Computer Science and Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University - Xi'an 710072, China
⁴ Unmanned Systems Research Institute, Northwestern Polytechnical University - Xi'an 710072, China
⁵ CNR Institute for Complex Systems - Via Madonna del Piano 10, 50019 Florence, Italy

^(a) li@nwpu.edu.cn
^(b) zhenwang0@gmail.com

Received: 28 March 2019
Accepted: 25 September 2019

Abstract

We study the influence of players' ability in promoting cooperation in a social dilemma game on interdependent networks. Namely, players of a network whose ability exceeds a given threshold are allowed to form additional links with corresponding players on another network. As individual ability is constantly updated, the resulting coupling architecture between the two networks is time-dependent. Our results demonstrate that such an interdependency helps cooperators to survive, and effectively alleviates the social dilemma by adjusting the coupling spontaneously. The coupling structure, and in particular the directionality of link between cooperators, plays a crucial role in this latter process. Finally, we reveal that the individuals' ability follows a power-law distribution whenever the system reaches a heterogeneous stable state, whereas it obeys a uniform distribution when the attained stable state is homogeneous.