Participation costs dismiss the advantage of heterogeneous networks in evolution of cooperation

TLDR

Social interactions occur on networks where individuals have varying numbers of contacts, and heterogeneity in connectivity has been shown to promote cooperation, but the cost of maintaining contacts can negate this benefit. In replicator dynamics, even a small participation cost removes the advantage of heterogeneous networks, causing highly connected players to earn less and less connected players to drive cooperation, while the cost is irrelevant in homogeneous populations.

Abstract

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. Under a common assumption of positively biased pay-off structure, well-connected players earn much by playing frequently, and cooperation once adopted by well-connected players is unbeatable and spreads to others. However, maintaining a social contact can be costly, which would prevent local pay-offs from being positively biased. In replicator-type evolutionary dynamics, it is shown that even a relatively small participation cost extinguishes the merit of heterogeneous networks in terms of cooperation. In this situation, more connected players earn less so that they are no longer spreaders of cooperation. Instead, those with fewer contacts win and guide the evolution. The participation cost, or the baseline pay-off, is irrelevant in homogeneous populations, but is essential for evolutionary games on heterogeneous networks.