Trudy Instituta Matematiki i Mekhaniki UrO RAN
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy Inst. Mat. i Mekh. UrO RAN:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, Volume 27, Number 3, Pages 71–86
DOI: https://doi.org/10.21538/0134-4889-2021-27-3-71-86
(Mi timm1839)
 

On one hybrid equilibrium

V. I. Zhukovskiia, K. N. Kudryavtsevb

a Lomonosov Moscow State University
b South Ural State University, Chelyabinsk
References:
Abstract: The notion of $BN$-hybrid equilibrium is proposed for a noncooperative $N$-person game. It is assumed that each player belongs to one of two classes: altruists and pragmatists. The altruists and the pragmatists choose their strategies using the concepts of the Berge equilibrium and the Nash equilibrium, respectively. Using a specially constructed Germeier convolution based on payoff functions, we obtain sufficient conditions for the existence of a $BN$-hybrid equilibrium. For an extension of the game with mixed strategies, a theorem on the existence of a $BN$-hybrid equilibrium is proved under constraints standard for mathematical game theory, namely, under the assumptions that the sets of the players' strategies are convex and compact and their payoff functions are continuous. The proposed concept is extended to noncooperative $N$-person games under interval uncertainty. An existence theorem is given for a strongly guaranteed $N$-hybrid equilibrium in mixed strategies.
Keywords: Nash equilibrium, Berge equilibrium, uncertainty, Germeier convolution.
Funding agency Grant number
Russian Foundation for Basic Research 20-41-740027
This work was supported jointly by the Russian Foundation for Basic Research and Chelyabinsk Oblast (project no. 20-41-740027).
Received: 21.04.2021
Revised: 28.05.2021
Accepted: 21.06.2021
Bibliographic databases:
Document Type: Article
UDC: 519.833
MSC: 91A06, 91A10
Language: Russian
Citation: V. I. Zhukovskii, K. N. Kudryavtsev, “On one hybrid equilibrium”, Trudy Inst. Mat. i Mekh. UrO RAN, 27, no. 3, 2021, 71–86
Citation in format AMSBIB
\Bibitem{ZhuKud21}
\by V.~I.~Zhukovskii, K.~N.~Kudryavtsev
\paper On one hybrid equilibrium
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2021
\vol 27
\issue 3
\pages 71--86
\mathnet{http://mi.mathnet.ru/timm1839}
\crossref{https://doi.org/10.21538/0134-4889-2021-27-3-71-86}
\elib{https://elibrary.ru/item.asp?id=46502691}
Linking options:
  • https://www.mathnet.ru/eng/timm1839
  • https://www.mathnet.ru/eng/timm/v27/i3/p71
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Trudy Instituta Matematiki i Mekhaniki UrO RAN
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024