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Decomposition of Games: Some Strategic Considerations

Author

Listed:
  • Joseph Abdou

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Nikolaos Pnevmatikos

    (LEMMA - Laboratoire d'économie mathématique et de microéconomie appliquée - Université Paris-Panthéon-Assas)

  • Marco Scarsini

    (LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma])

  • Xavier Venel

    (LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma])

Abstract

Orthogonal direct-sum decompositions of finite games into potential, harmonic and nonstrategic components exist in the literature. In this paper we study the issue of decomposing games that are strategically equivalent from a game-theoretical point of view, for instance games obtained via transformations such as duplications of strategies or positive affine mappings of the payoffs. We show the need to define classes of decompositions to achieve commutativity of game transformations and decompositions.

Suggested Citation

  • Joseph Abdou & Nikolaos Pnevmatikos & Marco Scarsini & Xavier Venel, 2022. "Decomposition of Games: Some Strategic Considerations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-04085301, HAL.
    • Handle: RePEc:hal:cesptp:hal-04085301
    DOI: 10.1287/moor.2021.1123
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    References listed on IDEAS

    as
    1. Osborne, Martin J & Rubinstein, Ariel, 1998. "Games with Procedurally Rational Players," American Economic Review, American Economic Association, vol. 88(4), pages 834-847, September.
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    3. Sandholm, William H., 2010. "Decompositions and potentials for normal form games," Games and Economic Behavior, Elsevier, vol. 70(2), pages 446-456, November.
    4. Adam Kalai & Ehud Kalai, 2013. "Cooperation in Strategic Games Revisited," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(2), pages 917-966.
    5. Candogan, Ozan & Ozdaglar, Asuman & Parrilo, Pablo A., 2013. "Dynamics in near-potential games," Games and Economic Behavior, Elsevier, vol. 82(C), pages 66-90.
    6. Ozan Candogan & Ishai Menache & Asuman Ozdaglar & Pablo A. Parrilo, 2011. "Flows and Decompositions of Games: Harmonic and Potential Games," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 474-503, August.
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    Cited by:

    1. Santiago Guisasola & Donald Saari, 2020. "With Potential Games, Which Outcome Is Better?," Games, MDPI, vol. 11(3), pages 1-20, August.

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