Cooperation conflicts with equality when allocating public goods

We consider coupled behavioural dynamics and edge dynamics. At each time step, an individual i is selected to update their strategy with probability p; whereas with probability 1 − p a link (i, j) is randomly selected, and broken with a probability that depends on the strategies adopted by individuals i and j. Accordingly, there are three rewiring probabilities: p CC , p CD (equal to p DC ), and p DD . To maintain the network’s connectivity, if either individual of the selected link has only a single neighbor, the link is re-selected at random. Because the networks may differ when evaluating fixation probabilities of cooperation (ρ C ) and defection (ρ D ), we adopt the absolute criterion ρ C > 1/N to determine when cooperation is favored by selection, rather than the relative criterion ρ C > ρ D . We present fixation probabilities estimated from 107 independent Monte Carlo simulations, and we use these probabilities to fit the critical benefit-to-cost ratio (b/c)* (vertical lines). The initial network structure is the Karate Club network. For each benefit factor δ, uniform allocation promotes cooperation while exacerbating inequality. This result demonstrates that the conflict between cooperation and equality persists under coevolution with dynamic edges. However, network rewiring can partly mitigate the conflict: the threshold required for cooperation, the Gini coefficient of resulting payoffs, and the fraction of individuals with negative returns w, are all lower than in the static case. For example, at δ = 1 and κ = 1, (b/c)* decreases from 1.43 in the baseline model to 1.41 in this dynamic setting, G decreases from 0.29 to 0.13, and w from 0.38 to 0.10. Parameters: θ = 0.03, p = 0.05, p CC = 0.1, p CD = 0.3, p DD = 0.5, c = 1.