Noisy Contagion Without Mutation

In a local interaction game agents play an identical stage game against their neighbours over time. For nearest neighbour interaction, it is established that, starting from a random initial configuration in which each agent has a positive probability of playing the risk dominant strategy, a sufficiently large population coordinates in the long-run on the risk dominant equilibrium almost surely. Our result improves on Blume (1995), Ellison (2000), and Morris (2000) by showing that the risk dominant equilibrium spreads to the entire population in a two dimensional lattice and without the help of mutation, as long as there is some randomness in the initial configuration