A Coordination Game in Scale-Free Networks

We study a coordination game in a network that indicates who plays with whom. A player chooses a strategy by logit choice. We show that in typical scale-free networks, one strategy always prevails by the neighborhood effect regardless of the values of parameters, while in regular networks, it prevails if and only if some condition is satisfied. In a scale-free network, people tend to choose the same strategy. We demonstrate that only a small number of players determine the strategy that prevails in this network. A model in a scale-free network is realistic because many real social networks are scale-free