A brief proof of the existence of an alpha-core for generalized strategic games. Full article
| Conference |
XXIV International conference “Mathematical Optimization Theory and Operations Research” 07-11 Jul 2025 , Новосибирск |
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| Journal |
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304 |
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| Output data | Year: 2025, Volume: 22, Number: 2, Pages: 46-53 Pages count : 8 DOI: 10.33048/semi.2025.C04, MSC 91A06, 91A10 | ||
| Tags | generalized strategic game, $\alpha$-core, Brouwer's fixed point theorem | ||
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0019 |
Abstract:
This paper studies the problem of whether an $\alpha$-core exists (is non-empty) for generalized normal-form games where player payoffs are described by point-to-set convex-valued, irreflexive, and weakly continuous preferences. We propose a short effective proof of the non-emptiness of the core; it based on a contradiction with Brouwer's theorem on the existence of a fixed point for a continuous mapping of a convex compact set into itself.
Cite:
Marakulin V.M.
A brief proof of the existence of an alpha-core for generalized strategic games.
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2025. V.22. N2. P.46-53. DOI: 10.33048/semi.2025.C04, MSC 91A06, 91A10
A brief proof of the existence of an alpha-core for generalized strategic games.
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2025. V.22. N2. P.46-53. DOI: 10.33048/semi.2025.C04, MSC 91A06, 91A10
Dates:
| Accepted: | Jun 1, 2025 |
| Published print: | Dec 31, 2025 |
| Published online: | Dec 31, 2025 |
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