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Diskretnyi Analiz i Issledovanie Operatsii, 2023, Volume 30, Issue 1, Pages 67–84
DOI: https://doi.org/10.33048/daio.2023.30.754
(Mi da1316)
 

On search of Nash equilibrium in quasiconcave quadratic games

I. M. Minarchenko

Melentiev Energy Systems Institute SB RAS, 130 Lermontov Street, 664033 Irkutsk, Russia
References:
Abstract: The Nash equilibrium problem with nonconcave quadratic payoff functions is considered. We analyze conditions which provide quasiconcavity of payoff functions in their own variables on the respective strategy sets and, consequently, guarantee existence of an equilibrium point. One of such conditions is that the matrix of every payoff function has exactly one positive eigenvalue; this condition is viewed as a basic assumption in the paper. We propose an algorithm that either converges to an equilibrium point or declares that the game has no equilibria. It is shown that some stages of the algorithm are noticeably simplified for quasiconcave games. The algorithm is tested on small-scale instances. Illustr. 1, bibliogr. 30.
Keywords: Nash equilibrium, quasiconcave functions, global optimization.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWEU-2021-0006 [АААА-А21-121012090034-3]
This research is carried out within the state assignment under the Program of Fundamental Research in Russia 2021–2030 (Project FWEU–2021–0006 [AAAA–A21–121012090034–3]).
Received: 29.09.2022
Revised: 29.09.2022
Accepted: 06.10.2022
Bibliographic databases:
Document Type: Article
UDC: 519.833.2
Language: Russian
Citation: I. M. Minarchenko, “On search of Nash equilibrium in quasiconcave quadratic games”, Diskretn. Anal. Issled. Oper., 30:1 (2023), 67–84; J. Appl. Industr. Math., 17:1 (2023), 120–130
Citation in format AMSBIB
\Bibitem{Min23}
\by I.~M.~Minarchenko
\paper On search of Nash equilibrium in~quasiconcave~quadratic games
\jour Diskretn. Anal. Issled. Oper.
\yr 2023
\vol 30
\issue 1
\pages 67--84
\mathnet{http://mi.mathnet.ru/da1316}
\crossref{https://doi.org/10.33048/daio.2023.30.754}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4569858}
\transl
\jour J. Appl. Industr. Math.
\yr 2023
\vol 17
\issue 1
\pages 120--130
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