Perturbation theory for evolution of cooperation on networks
Abstract
Network structure is a mechanism for promoting cooperation in social dilemma games. In the present study, we explore graph surgery, i.e., to slightly perturb the given network, towards a network that better fosters cooperation. To this end, we develop a perturbation theory to assess the change in the propensity of cooperation when we add or remove a single edge to the given network. Our perturbation theory is for a previously proposed randomwalkbased theory that provides the threshold benefittocost ratio, $(b/c)^*$, which is the value of the benefittocost ratio in the donation game above which the cooperator is more likely to fixate than in the control case, for any finite networks. We find that $(b/c)^*$ decreases when we remove a single edge in a majority of cases and that our perturbation theory captures at a reasonable accuracy which edge removal makes $(b/c)^*$ small to facilitate cooperation. In contrast, $(b/c)^*$ tends to increase when we add an edge, and the perturbation theory is not good at predicting the edge addition that changes $(b/c)^*$ by a large amount. Our perturbation theory significantly reduces the computational complexity for calculating the outcome of graph surgery.
 Publication:

arXiv eprints
 Pub Date:
 August 2022
 DOI:
 10.48550/arXiv.2208.06584
 arXiv:
 arXiv:2208.06584
 Bibcode:
 2022arXiv220806584M
 Keywords:

 Physics  Physics and Society
 EPrint:
 21 pages, 4 figures