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Graphical potential games

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  • Babichenko, Yakov
  • Tamuz, Omer

Abstract

We study the class of potential games that are also graphical games with respect to a given graph G of connections between the players. We show that, up to strategic equivalence, this class of games can be identified with the set of Markov random fields on G. From this characterization, and from the Hammersley–Clifford theorem, it follows that the potentials of such games can be decomposed into local potentials.

Suggested Citation

  • Babichenko, Yakov & Tamuz, Omer, 2016. "Graphical potential games," Journal of Economic Theory, Elsevier, vol. 163(C), pages 889-899.
    • Handle: RePEc:eee:jetheo:v:163:y:2016:i:c:p:889-899
    DOI: 10.1016/j.jet.2016.03.010
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    References listed on IDEAS

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    1. Yann Bramoull? & Rachel Kranton & Martin D'Amours, 2014. "Strategic Interaction and Networks," American Economic Review, American Economic Association, vol. 104(3), pages 898-930, March.
    2. Nisan,Noam & Roughgarden,Tim & Tardos,Eva & Vazirani,Vijay V. (ed.), 2007. "Algorithmic Game Theory," Cambridge Books, Cambridge University Press, number 9780521872829, January.
    3. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
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    Cited by:

    1. Xinrong Yang & Zhenping Geng & Haitao Li, 2023. "Matrix-Based Method for the Analysis and Control of Networked Evolutionary Games: A Survey," Games, MDPI, vol. 14(2), pages 1-13, February.
    2. Simone Cerreia-Vioglio & Roberto Corrao & Giacomo Lanzani, 2020. "Robust Opinion Aggregation and its Dynamics," Working Papers 662, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    3. Mehmet S. Ismail & Ronald Peeters, 2024. "A connection between von Neumann-Morgenstern expected utility and symmetric potential games," Theory and Decision, Springer, vol. 97(4), pages 707-720, December.
    4. Nikolaos Nagkoulis & Konstantinos L. Katsifarakis, 2022. "Using Game Theory to Assign Groundwater Pumping Schedules," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(5), pages 1571-1586, March.
    5. Toru Kitagawa & Guanyi Wang, 2023. "Individualized Treatment Allocation in Sequential Network Games," Papers 2302.05747, arXiv.org, revised Jul 2024.

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    Keywords

    Potential games; Graphical games;

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