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Robust Nash equilibria in vector-valued games with uncertainty

Author

Listed:
  • Giovanni P. Crespi

    (Universitá degli Studi dell’Insubria)

  • Daishi Kuroiwa

    (Shimane University)

  • Matteo Rocca

    (Universitá degli Studi dell’Insubria)

Abstract

We study a vector-valued game with uncertainty in the pay-off functions. We reduce the notion of Nash equilibrium to a robust set optimization problem and we define accordingly the notions of robust Nash equilibria and weak robust Nash equilibria. Existence results for the latter are proved and a comparison between the former and the analogous notion in Yu and Liu (J Optim Theory Appl 159:272–280, 2013) is shown with an example. The proposed definition of weak robust Nash equilibrium is weaker than that already introduced in Yu and Liu (2013). On the contrary, the robust Nash equilibrium we introduce is not comparable with the notion of robust equilibrium in Yu and Liu (2013), that is defined componentwise. Nevertheless, by means of an example, we show that our notion has some advantages, avoiding some pitfalls that occurs with the other.

Suggested Citation

  • Giovanni P. Crespi & Daishi Kuroiwa & Matteo Rocca, 2020. "Robust Nash equilibria in vector-valued games with uncertainty," Annals of Operations Research, Springer, vol. 289(2), pages 185-193, June.
    • Handle: RePEc:spr:annopr:v:289:y:2020:i:2:d:10.1007_s10479-020-03563-2
    DOI: 10.1007/s10479-020-03563-2
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    References listed on IDEAS

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    1. Levaggi, Laura & Pusillo, Lucia, 2017. "Classes of multiojectives games possessing Pareto equilibria," Operations Research Perspectives, Elsevier, vol. 4(C), pages 142-148.
    2. Giovanni Paolo Crespi & Davide Radi & Matteo Rocca, 2017. "Robust games: theory and application to a Cournot duopoly model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 177-198, November.
    3. Xie Ding, 2012. "Equilibrium existence theorems for multi-leader-follower generalized multiobjective games in FC-spaces," Journal of Global Optimization, Springer, vol. 53(3), pages 381-390, July.
    4. Lucia Pusillo, 2017. "Vector Games with Potential Function," Games, MDPI, vol. 8(4), pages 1-11, September.
    5. Giovanni P. Crespi & Daishi Kuroiwa & Matteo Rocca, 2017. "Quasiconvexity of set-valued maps assures well-posedness of robust vector optimization," Annals of Operations Research, Springer, vol. 251(1), pages 89-104, April.
    6. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    7. H. Yu & H. M. Liu, 2013. "Robust Multiple Objective Game Theory," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 272-280, October.
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