Robust Nash equilibria in vector-valued games with uncertainty

Giovanni P. Crespi (), Daishi Kuroiwa () and Matteo Rocca ()
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Giovanni P. Crespi: Universitá degli Studi dell’Insubria
Daishi Kuroiwa: Shimane University
Matteo Rocca: Universitá degli Studi dell’Insubria

Annals of Operations Research, 2020, vol. 289, issue 2, No 3, 185-193

Abstract: 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.

Keywords: Vector-valued game; Uncertainty; Robust solution; Nash equilibria; Set optimization; 91A10; 93D09; 90C29 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10479-020-03563-2

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