Skip to content
DraconiticResearch
Search Sources API
201,642 studies31 sourcesUpdated 14 min ago
PreprintCC BY 4.0arXiv

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

  • Urairat Deepan
  • Poom Kumam
  • Parin Chaipunya
Open at sourcePDFDOICite

Abstract

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.

Related

  1. Existence of Reeb Chords from the Generation-Criteria
    Mohamad Rabah
    arXivPreprintCC0Full textGeometry & topologyarXiv
  2. Sharp criteria for the existence of solutions to curvature equations with two singular sources on rectangular torus
    Zhijie Chen, Zhen Song
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. Semigroup Criteria for Blow-up and Global Existence of Semilinear Heat Equations on Metric Measure Spaces
    Giulia Meglioli, Fabio Punzo
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. On the Existence of Pressure-Equilibrium-Preserving Numerical Fluxes for Supercritical Fluids
    Robin Ben Klein
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingarXiv
  5. Commutativity Criteria and Structural Properties of Prime Near-Rings Admitting Right Generalized Derivations on Specific Ideals
    Khaled Aldwoah, Inzamam ul Huque, Hafedh Alnoghashi +3
    AxiomsPeer-reviewedCC BY 4.0Algebra & number theoryCrossref

Cite

BibTeXRIS
BibTeX
@misc{deepan2026stability,
  title = {{Stability of ideal Nash equilibrium points in generalized multi-criteria games, interval-valued games, and existence in single-leader--multi-follower problems}},
  author = {Urairat Deepan and Poom Kumam and Parin Chaipunya},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41439},
  eprint = {2610.41439},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41439},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Stability of ideal Nash equilibrium points in generalized multi-criteria games, interval-valued games, and existence in single-leader--multi-follower problems
AU  - Urairat Deepan
AU  - Poom Kumam
AU  - Parin Chaipunya
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41439
UR  - https://arxiv.org/abs/2610.41439
AB  - 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.
ER  -