In a local interaction game agents play an identical stage game against their neighbors over time. For nearest neighbor 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(1996), and Morris(1997) 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.