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On approximate mixed Nash equilibria and average marginal functions for two-stage three-players games

In: Optimization with Multivalued Mappings

Author

Listed:
  • Lina Mallozzi

    (Università di Napoli “Federico II”)

  • Jacqueline Morgan

    (Università di Napoli “Federico II”)

Abstract

Summary In this paper we consider a two-stage three-players game: in the first stage one of the players chooses an optimal strategy knowing that, at the second stage, the other two players react by playing a noncooperative game which may admit more than one Nash equilibrium. We investigate continuity properties of the set-valued function defined by the Nash equilibria of the (second stage) two players game and of the marginal functions associated to the first stage optimization problem. By using suitable approximations of the mixed extension of the Nash equilibrium problem, we obtain without convexity assumption the lower semicontinuity of the set-valued function defined by the considered approximate Nash equilibria and the continuity of the associate approximate average marginal functions when the second stage corresponds to a particular class of noncooperative games called antipotential games.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:spochp:978-0-387-34221-4_5
    DOI: 10.1007/0-387-34221-4_5
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    Citations

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    Cited by:

    1. Lina Mallozzi & Armando Sacco, 2022. "Stackelberg-Nash equilibrium and quasi harmonic games," Annals of Operations Research, Springer, vol. 318(2), pages 1029-1041, November.
    2. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2020. "Best response algorithms in ratio-bounded games: convergence of affine relaxations to Nash equilibria," CSEF Working Papers 593, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.

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