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.

Electronic Proceedings in Theoretical Computer Science
The 15th Conference on Theoretical Aspects of Rationality and Knowledge (TARK)
This work was funded by the The Netherlands Organisation for Scientific Research (NWO); grant id nwo/612.001.352 - Combining Machine Learning and Game-theoretic Approaches for Cluster Analysis
CWI management

Apt, K.R, Simon, S.E, & Wojtczak, D.K. (2016). Coordination games on directed graphs. In Electronic Proceedings in Theoretical Computer Science. doi:10.4204/EPTCS.215.6