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Stability of ideal Nash equilibrium points in generalized multi-criteria games, interval-valued games, and existence in single-leader--multi-follower problems — arXiv:2610.41439

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.41439
License (as archived): CC0-1.0
Archived: 2026-11-03T05:43:11.491Z
SHA-256 of the archived text: 9464c6ae4791a6efb5da3ff763ad6fe880b7186541cdc076acbd4f3d160bfa22
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How to cite

Stability of ideal Nash equilibrium points in generalized multi-criteria games, interval-valued games, and existence in single-leader--multi-follower problems — arXiv:2610.41439 — arXiv (en), https://arxiv.org/abs/2610.41439 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_53bcda491e5e (Metraipolis archive dc_53bcda491e5e, sha256 9464c6ae4791a6efb5da3ff763ad6fe880b7186541cdc076acbd4f3d160bfa22)

BibTeX

@misc{dc53bcda491e5e,
  title = {Stability of ideal Nash equilibrium points in generalized multi-criteria games, interval-valued games, and existence in single-leader--multi-follower problems — arXiv:2610.41439},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.41439},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_53bcda491e5e; sha256 9464c6ae4791a6efb5da3ff763ad6fe880b7186541cdc076acbd4f3d160bfa22},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.41439. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study the stability of ideal Nash equilibria in generalized multi-criteria games, in which each player's vector-valued payoff is ordered by a closed cone and the feasible strategy sets depend on the other players' strategies. Under compactness and continuity assumptions, the ideal Nash equilibrium correspondence is upper semicontinuous on the class of games admitting an ideal equilibrium. Our main result does not require the ordering cones to be convex or pointed. In fact, the ideal equilibria are exactly the common equilibria of associated scalar games when all the cones are convex. As consequences of our results, the stability of interval-valued games is derived and existence theorems for single-leader-multi-follower problems are proved for both optimistic and pessimistic sense.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.OC, nuovi lavori del giorno).
Categorie arXiv: Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2610.41439 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T05:31:17.164Z dalla pagina https://arxiv.org/list/math.OC/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).