Heterogeneous Networks in Evolution of Cooperation

Real social interactions occur on networks in which each individual is connected to some, but not all, of others. In social dilemma games with a fixed population size, heterogeneity in the number of contacts per player is known to promote evolution of cooperation. An essential assumption underlying this phenomenon is positively biased payoff structure so that more connected players earn more by playing more frequently. Then cooperation once adopted by well-connected players is unbeatable and spreads to others. However, maintaining a social contact can be costly in real lives, which would prevent local payoffs from being positively biased. We show that even a relatively small participation cost extinguishes the promoted altruism on heterogeneous networks in replicator-type evolutionary dynamics. In this situation, more connected players are charged more so that they are no longer spreaders of cooperation. If participation is even more costly, those with fewer contacts win and guide the evolution. The participation cost, or the baseline payoff, is irrelevant in homogeneous populations but a key factor for describing evolutionary games on heterogeneous networks.