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Anti-coordination Games and Stable Graph Colorings

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Algorithmic Game Theory (SAGT 2013)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 8146))

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Abstract

Motivated by understanding non-strict and strict pure strategy equilibria in network anti-coordination games, we define notions of stable and, respectively, strictly stable colorings in graphs. We characterize the cases when such colorings exist and when the decision problem is NP-hard. These correspond to finding pure strategy equilibria in the anti-coordination games, whose price of anarchy we also analyze. We further consider the directed case, a generalization that captures both coordination and anti-coordination. We prove the decision problem for non-strict equilibria in directed graphs is NP-hard. Our notions also have multiple connections to other combinatorial questions, and our results resolve some open problems in these areas, most notably the complexity of the strictly unfriendly partition problem.

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Kun, J., Powers, B., Reyzin, L. (2013). Anti-coordination Games and Stable Graph Colorings. In: Vöcking, B. (eds) Algorithmic Game Theory. SAGT 2013. Lecture Notes in Computer Science, vol 8146. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41392-6_11

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  • DOI: https://doi.org/10.1007/978-3-642-41392-6_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41391-9

  • Online ISBN: 978-3-642-41392-6

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