Summary: This paper compares local and global strategic interaction when players update using the (myopic) best-response rule. I show that randomizing the order in which players update their strategic choice suffices to achieve coordination on the risk-dominant strategy in symmetric \(2\times 2\) coordination games. The “persistant randomness” which is necessary to achieve similar coordination with global interaction is replaced under local interaction by spatial variation in the initial condition. An extension of the risk-dominance idea gives the same convergence result for \(K\times K\) games with strategic complementarities. Similar results for \(K\times K\) pure coordination games and potential games are also presented.