Fence-sitters Protect Cooperation in Complex Networks

TL;DR

This paper introduces a vectorial approach to analyze evolutionary game dynamics in complex networks, highlighting how fence-sitters—individuals who change strategies—can promote cooperation, especially when considering payoff memory effects.

Contribution

It develops an analytical vectorial framework for all two-strategy games and reveals the nontrivial role of fence-sitters in sustaining cooperation in complex networks.

Findings

Payoff memory controls fence-sitters' influence and cooperation levels.

Fence-sitters indirectly protect cooperation in complex topologies.

The formalism applies broadly to two-strategy evolutionary games.

Abstract

Evolutionary game theory is one of the key paradigms behind many scientific disciplines from science to engineering. In complex networks, because of the difficulty of formulating the replicator dynamics, most of previous studies are confined to a numerical level. In this paper, we introduce a vectorial formulation to derive three classes of individuals' payoff analytically. The three classes are pure cooperators, pure defectors, and fence-sitters. Here, fence-sitters are the individuals who change their strategies at least once in the strategy evolutionary process. As a general approach, our vectorial formalization can be applied to all the two-strategies games. To clarify the function of the fence-sitters, we define a parameter, payoff memory, as the number of rounds that the individuals' payoffs are aggregated. We observe that the payoff memory can control the fence-sitters' effects and the level of cooperation efficiently. Our results indicate that the fence-sitters' role is nontrivial in the complex topologies, which protects cooperation in an indirect way. Our results may provide a better understanding of the composition of cooperators in a circumstance where the temptation to defect is larger.