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Potential games with incomplete preferences

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  • Park, Jaeok

Abstract

This paper studies potential games allowing the possibility that players have incomplete preferences and empty best-response sets. We define four notions of potential games, ordinal, generalized ordinal, best-response, and generalized best-response potential games, and characterize them using cycle conditions. We study Nash equilibria of potential games and show that the set of Nash equilibria remains the same when every player’s preferences are replaced with the smallest generalized (best-response) potential relation or a completion of it. Similar results are established about strict Nash equilibria of ordinal and best-response potential games. Lastly, we examine the relations among the four notions of potential games as well as pseudo-potential games.

Suggested Citation

  • Park, Jaeok, 2015. "Potential games with incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 58-66.
    • Handle: RePEc:eee:mateco:v:61:y:2015:i:c:p:58-66
    DOI: 10.1016/j.jmateco.2015.07.007
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    References listed on IDEAS

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    1. Kukushkin, Nikolai S., 1999. "Potential games: a purely ordinal approach," Economics Letters, Elsevier, vol. 64(3), pages 279-283, September.
    2. Kukushkin, Nikolai S., 2004. "Best response dynamics in finite games with additive aggregation," Games and Economic Behavior, Elsevier, vol. 48(1), pages 94-110, July.
    3. Dubey, Pradeep & Haimanko, Ori & Zapechelnyuk, Andriy, 2006. "Strategic complements and substitutes, and potential games," Games and Economic Behavior, Elsevier, vol. 54(1), pages 77-94, January.
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    8. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
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    10. Henk Norde & Fioravante Patrone, 2001. "A potential approach for ordinal games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(1), pages 69-75, June.
    11. 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. Abheek Ghosh & Paul W. Goldberg, 2023. "Best-Response Dynamics in Lottery Contests," Papers 2305.10881, arXiv.org.
    2. Ewerhart, Christian, 2017. "The lottery contest is a best-response potential game," Economics Letters, Elsevier, vol. 155(C), pages 168-171.
    3. De Magistris, Enrico, 2024. "Incomplete preferences or incomplete information? On Rationalizability in games with private values," Games and Economic Behavior, Elsevier, vol. 144(C), pages 126-140.
    4. Andreas H. Hamel & Andreas Löhne, 2018. "A set optimization approach to zero-sum matrix games with multi-dimensional payoffs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(3), pages 369-397, December.
    5. Amparo M. Mármol & Luisa Monroy & M. Ángeles Caraballo & Asunción Zapata, 2017. "Equilibria with vector-valued utilities and preference information. The analysis of a mixed duopoly," Theory and Decision, Springer, vol. 83(3), pages 365-383, October.
    6. Juho Kokkala & Kimmo Berg & Kai Virtanen & Jirka Poropudas, 2019. "Rationalizable strategies in games with incomplete preferences," Theory and Decision, Springer, vol. 86(2), pages 185-204, March.
    7. Achim Hagen & Pierre von Mouche & Hans-Peter Weikard, 2020. "The Two-Stage Game Approach to Coalition Formation: Where We Stand and Ways to Go," Games, MDPI, vol. 11(1), pages 1-31, January.

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