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Stackelberg-Nash equilibrium and quasi harmonic games

Author

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  • Lina Mallozzi

    (University of Naples Federico II)

  • Armando Sacco

    (University of Naples “Parthenope”)

Abstract

Security solutions for two stage games, where the second stage consists of a strategic form noncooperative game, are not reachable in many problems. The aim of this paper is to investigate such solutions. Mixed extension for the second stage game is considered and existence results for approximate mixed security solutions, together with the convergences of values, are given and illustrated by significative examples. The results apply to the class of quasi harmonic games.

Suggested Citation

  • Lina Mallozzi & Armando Sacco, 2022. "Stackelberg-Nash equilibrium and quasi harmonic games," Annals of Operations Research, Springer, vol. 318(2), pages 1029-1041, November.
    • Handle: RePEc:spr:annopr:v:318:y:2022:i:2:d:10.1007_s10479-020-03916-x
    DOI: 10.1007/s10479-020-03916-x
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    References listed on IDEAS

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    1. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    2. 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.
    3. Hanif D. Sherali & Allen L. Soyster & Frederic H. Murphy, 1983. "Stackelberg-Nash-Cournot Equilibria: Characterizations and Computations," Operations Research, INFORMS, vol. 31(2), pages 253-276, April.
    4. Lina Mallozzi & Jacqueline Morgan, 2006. "On approximate mixed Nash equilibria and average marginal functions for two-stage three-players games," Springer Optimization and Its Applications, in: Stephan Dempe & Vyacheslav Kalashnikov (ed.), Optimization with Multivalued Mappings, pages 97-107, Springer.
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