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 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)
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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

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
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