Dynamic Matching Pennies on Networks

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). Our results imply that the network structure generally plays a very crucial role in determining LLC. When the network is a line or a ring, for almost all type configurations, LLC=1, meaning that a pure strategy Nash equilibrium is reached, regardless of the initial action profiles. However, when the network is a star, LLC=4 for approximately half of the type configurations. The ordinal potential property and the sequential best response dynamic are also studied