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Title: Robust Nash equilibria in vector-valued games with uncertainty
Authors: Crespi, Giovanni Paolo
Kuroiwa, Daishi
Rocca, Matteo
Issue Date: 2020
Publisher: Springer Science+Business Media
Bibliographic citation: Crespi Giovanni Paolo, Kuroiwa Daishi, Rocca Matteo (2020), Robust Nash equilibria in vector-valued games with uncertainty. In: Annals of operations research. Published electronically 13 March 2020. ISSN 0254-5330. E-ISSN 1572-9338. DOI 10.1007/s10479-020-03563-2.
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.
Journal/Book: Annals of operations research
ISSN: 0254-5330
Appears in Collections:Contributo in rivista

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