Imitation Dynamics in Population Games Over Large-Scale Networks

We study imitation-based evolutionary dynamics in potential population games. These are modeled as a discrete-time Markov chain whose state is the action profile of all agents. Although each agent's reward is determined by the underlying population game, we introduce an imitation mechanism that operates along the edges of a given network. Specifically, during each imitation step, an agent adopts the action of a neighboring agent with a probability that depends on the difference in their rewards. To ensure ergodicity of the Markov chain, we incorporate a spontaneous mutation mechanism, allowing each agent to randomly change their action with a small probability.We then analyze the so called large population double limit, where, first, the number of agents tends to infinity and, second, the mutation intensity tends to zero. Under a suitable set of assumptions, we prove that the invariant distribution of the Markov chain concentrates on the set of Nash equilibria of the potential population game.