title: Fence-sitters protect cooperation in complex networks.
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 the 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-strategy 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.
authors.affiliation: Univ Normandy, France; ULH, LMAH, F-76600 Le Havre, FR CNRS 3335, ISCN, 25 rue Philippe Lebon, 76600 Le Havre, France and Department of Computer Science, University College London, Gower Street, London, WC1E 6BT, United Kingdom.
authors.forename: Yichao
authors.initials: Y
authors.lastname: Zhang
authors.forename: M A
authors.initials: MA
authors.lastname: Aziz-Alaoui
authors.forename: Cyrille
authors.initials: C
authors.lastname: Bertelle
authors.forename: Shi
authors.initials: S
authors.lastname: Zhou
authors.forename: Wenting
authors.initials: W
authors.lastname: Wang