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 Inst. Mat. i Mekh. UrO RAN, 2018, Volume 24, Number 2, Pages 64–75 (Mi timm1524)  

On the solution of a differential game of managing the investments in an advertising campaign

E. V. Gromovaab, D. Gromovb, Yu. E. Lakhinab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Saint Petersburg State University

Abstract: We consider a differential game of managing the investments in an advertising campaign for the case of n symmetric players. The problem is solved in the class of positional strategies both for the cooperative statement, where the players agree on using controls that maximize the total payoff before the game starts, and for the noncooperative statement, in which the Nash equilibrium is used as a solution. It is shown that the solution of the problem is not unique in both cases. One candidate function is found by means of a detailed analysis. Then the solution is chosen with the use of an economic criterion described by Bass, Krishnamoorthy, Prasad, and Sethi in 2005. The solutions chosen earlier are in complete agreement with the choice with respect to the economic criterion.

Keywords: non-zero-sum differential games, Nash equiiibrium, advertising model.

Funding Agency Grant Number
Russian Science Foundation 17-11-01093


DOI: https://doi.org/10.21538/0134-4889-2018-24-2-64-75

Full text: PDF file (225 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2019, 305, suppl. 1, S75–S85

Bibliographic databases:

UDC: 519.83
MSC: 91A23, 90B60
Received: 03.03.2018

Citation: E. V. Gromova, D. Gromov, Yu. E. Lakhina, “On the solution of a differential game of managing the investments in an advertising campaign”, Trudy Inst. Mat. i Mekh. UrO RAN, 24, no. 2, 2018, 64–75; Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S75–S85

Citation in format AMSBIB
\Bibitem{GroGroLak18}
\by E.~V.~Gromova, D.~Gromov, Yu.~E.~Lakhina
\paper On the solution of a differential game of managing the investments in an advertising campaign
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2018
\vol 24
\issue 2
\pages 64--75
\mathnet{http://mi.mathnet.ru/timm1524}
\crossref{https://doi.org/10.21538/0134-4889-2018-24-2-64-75}
\elib{http://elibrary.ru/item.asp?id=35060679}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2019
\vol 305
\issue , suppl. 1
\pages S75--S85
\crossref{https://doi.org/10.1134/S0081543819040096}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000451633100008}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85073509169}


Linking options:
  • http://mi.mathnet.ru/eng/timm1524
  • http://mi.mathnet.ru/eng/timm/v24/i2/p64

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
    Number of views:
    This page:129
    Full text:35
    References:15
    First page:5

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020