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Decomposition of Games: Some Strategic Considerations

Author

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  • Joseph Abdou

    (Centre d’Économie de la Sorbonne, Université Paris 1, Panthéon-Sorbonne, 75647 Paris Cedex 13, France)

  • Nikolaos Pnevmatikos

    (Laboratoire d’Économie Mathématique et de Microéconomie Appliquée, Université Paris 2, Panthéon-Assas, 75006 Paris, France)

  • Marco Scarsini

    (Dipartimento di Economia e Finanza, Luiss University, 00197 Rome, Italy)

  • Xavier Venel

    (Dipartimento di Economia e Finanza, Luiss University, 00197 Rome, Italy)

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," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 176-208, February.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:1:p:176-208
    DOI: 10.1287/moor.2021.1123
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    References listed on IDEAS

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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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