Volume 142, Number 6, June 2023
|Number of page(s)
|Mathematical and interdisciplinary physics
|23 June 2023
Unexpected paths to cooperation on tied hyperbolic networks
1 Faculty of Natural Sciences and Mathematics, University of Maribor - Koroška cesta 160, 2000 Maribor, Slovenia
2 Faculty of Medicine, University of Maribor - Taborska ulica 8, 2000 Maribor, Slovenia
3 Department of Medical Research, China Medical University Hospital, China Medical University - Taichung, Taiwan
4 Alma Mater Europaea - Slovenska ulica 17, 2000 Maribor, Slovenia
5 Complexity Science Hub Vienna - Josefstädterstraße 39, 1080 Vienna, Austria
6 Department of Physics, Kyung Hee University - 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, Republic of Korea
(a) E-mail: firstname.lastname@example.org (corresponding author)
Received: 23 May 2023
Accepted: 7 June 2023
Hyperbolic networks have high clustering, short average path lengths, and community structure, which are all properties that are commonly associated with social networks. As such, these networks constitute the perfect playing ground for probing factors that may affect public cooperation in realistic scenarios. And although much is already known about the evolution of cooperation on networks, we here consider the public goods game on tied hyperbolic networks, such that payoffs in one network layer influence the payoffs in the other and vice versa. We also consider random, assortative, and disassortative mixing in the networks to account for varying connections between players over time. While our research confirms the overall positive impact of interdependent payoffs, we also find that mixing on the network where cooperation thrives may strongly promote the cooperation in the other network, while destroying it completely in the former. We show that this is related to the mapping of lower payoffs from one network to the other, where cooperators in one network benefit from the failure of cooperators in the other network. Namely, as soon as the multiplication factor for the public goods is high enough to nullify the negative effects of mixing and cooperators thus recover, the positive effect on cooperation in the other network vanishes. We determine optimal conditions for this phenomenon in terms of the frequency of mixing and the strength of ties between the payoffs on both networks, and we discuss the implications of our research for enhanced cooperation in coupled populations, in particular in the light of mutual success not always being desirable for cooperation to thrive.
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