I continue the study, begun in Blume (1993), of stochastic strategy revision processes in large player populations where the range of interaction between players is small. Each player interacts directly with only a finite set of neighbors, but any two players indirectly interact through a finite chain of direct interactions. The purpose of this paper is to compare local strategic interaction with global strategic interaction when players update their choice according to the (myopic) best-response rule. I show that randomizing the order in which players update their strategic choice is sufficient to achieve coordination on the risk-dominant strategy in symmetric 2 x 2 coordination games. The "persistant randomness" which is necessary to achieve similar coordination when the range of interaction is global is replaced by spatial variation in choice in the initial condition when strategic interactions are local. An extension of the risk-dominance idea gives the same convergence result for K x K games with strategic complementarities. Similar results for K x K pure coordination games and potential games are also presented.