Coordination Games on Directed Graphs
  We study natural strategic games on directed graphs, which capture the idea of coordination in the absence of globally common strategies. We show that these games do not need to have a pure Nash equilibrium and that the problem of determining their existence is NP-complete. The same holds for strong equilibria. We also exhibit some classes of games for which strong equilibria exist and prove that a strong equilibrium can then be found in linear time. 
Krzysztof R. Apt (Centrum Wiskunde and Informatica, Amsterdam, The   Netherlands), Sunil Simon (Department of CSE, IIT Kanpu...
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