Dynamic matching pennies on networks

Zhigang Cao, Cheng-Zhong Qin, Xiaoguang Yang, Boyu Zhang

Abstract: We consider a network game based on matching pennies with two types of agents, conformists and rebels. Conformists prefer to match the action taken by the majority of her neighbors while rebels like to match the minority. We investigate the simultaneous best response dynamic focusing on the lengths of limit cycles (LLC for short). We show that \(\hbox {LLC}=1\) or 2 when all agents are of the same type, and \(\hbox {LLC}=4\) when there is no conformist-rebel edge and no two even-degreed agents (if any) are neighboring each other. Moreover, \(\hbox {LLC}=1\) for almost all type configurations when the network is a line or a ring, which implies that a pure strategy Nash equilibrium is reached from any initial action profile. However, \(\hbox {LLC}=4\) for about one half of the type configurations with star networks.