Deterministic theory of evolutionary games on temporal networks

Author:

Wang Xiaofeng12ORCID,Fu Feng34ORCID,Wang Long5ORCID

Affiliation:

1. Department of Automation, School of Information Science and Technology, Donghua University , Shanghai 201620, People's Republic of China

2. Engineering Research Center of Digitized Textile and Apparel Technology (Ministry of Education), Donghua University , Shanghai 201620, People's Republic of 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

5. Center for Systems and Control, College of Engineering, Peking University , Beijing 100871, People's Republic of China

Abstract

Recent empirical studies have revealed that social interactions among agents in realistic networks merely exist intermittently and occur in a particular sequential order. However, it remains unexplored how to theoretically describe evolutionary dynamics of multiple strategies on temporal networks. Herein, we develop a deterministic theory for studying evolutionary dynamics of any n × n pairwise games in structured populations where individuals are connected and organized by temporally activated edges. In the limit of weak selection, we derive replicator-like equations with a transformed payoff matrix characterizing how the mean frequency of each strategy varies over time, and then obtain critical conditions for any strategy to be evolutionarily stable on temporal networks. Interestingly, the re-scaled payoff matrix is a linear combination of the original payoff matrix with an additional one describing local competitions between any pair of different strategies, whose weights are solely determined by network topology and selection intensity. As a particular example, we apply the deterministic theory to analysing the impacts of temporal networks in the mini-ultimatum game, and find that temporally networked population structures result in the emergence of fairness. Our work offers theoretical insights into the subtle effects of network temporality on evolutionary game dynamics.

Funder

National Natural Science Foundation of China

Publisher

The Royal Society

Reference49 articles.

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