This paper analyzes players’ long-run behavior in evolutionary coordination games with imitation and one-dimensional local interaction. Players are assumed to interact with their two neighbors and to imitate actions with the highest average payoffs. We find that the payoff-dominant equilibrium survives in the long run with positive probability. The results derive the conditions under which both risk-dominant-strategy and payoff-dominant-strategy takers co-exist in the long run. The risk-dominant equilibrium is the unique long-run equilibrium for the remaining cases. This study extends and complements the analyses of Eshel et al. (Am Econ Rev 88:157–179, <CitationRef CitationID="CR14">1998</CitationRef>) and Vega-Redondo (Evolution, games, and economic behaviour, <CitationRef CitationID="CR21">1996</CitationRef>). Combining Alós-Ferrer and Weidenholzer’s (Econ Lett 93:163–168, <CitationRef CitationID="CR1">2006</CitationRef>; J Econ Theory 14:251–274, <CitationRef CitationID="CR2">2008</CitationRef>) and our results, we conclude that players’ long-run behavior varies with imitation rules and information collecting modes. Finally, we show the convergence rate to all the long-run equilibria. Copyright Springer-Verlag Berlin Heidelberg 2013
