Long-run equilibria, dominated strategies, and local interactions

We revisit a result by Kim and Wong (2010) showing that under global interactions any strict Nash equilibrium of a coordination game can be supported as long run equilibrium by properly adding dominated strategies. We show that in the circular city model of local interactions and in the torus model of local interactions the selection of 12-dominant strategies remains when adding strictly dominated strategies if interaction is sufficiently local. Conversely, if the local interaction structure is “central” in the circular city model any equilibrium strategy of the original game can be supported as long run equilibrium by adding properly suited dominated strategies.