### 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 et al. in 2005. The solutions chosen earlier are in complete agreement with the choice with respect to the economic criterion.

Original language | English |
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Pages (from-to) | S75-S85 |

Journal | Proceedings of the Steklov Institute of Mathematics |

Volume | 305 |

Issue number | Suppl 1 |

DOIs | |

Publication status | Published - Jul 2019 |

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### Scopus subject areas

- Mathematics (miscellaneous)

### Cite this

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**On the Solution of a Differential Game of Managing the Investments in an Advertising Campaign.** / Gromova, E. V. ; Gromov, D. V. ; Lakhina, Yu. E. .

Research output

TY - JOUR

T1 - On the Solution of a Differential Game of Managing the Investments in an Advertising Campaign

AU - Gromova, E. V.

AU - Gromov, D. V.

AU - Lakhina, Yu. E.

N1 - Gromova, E.V., Gromov, D.V. & Lakhina, Y.E. Proc. Steklov Inst. Math. (2019) 305(Suppl 1): S75. https://doi.org/10.1134/S0081543819040096

PY - 2019/7

Y1 - 2019/7

N2 - 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 et al. in 2005. The solutions chosen earlier are in complete agreement with the choice with respect to the economic criterion.

AB - 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 et al. in 2005. The solutions chosen earlier are in complete agreement with the choice with respect to the economic criterion.

KW - advertising model

KW - Nash equilibrium

KW - nonzero-sum differential games

UR - http://www.scopus.com/inward/record.url?scp=85073509169&partnerID=8YFLogxK

U2 - 10.1134/S0081543819040096

DO - 10.1134/S0081543819040096

M3 - статья

AN - SCOPUS:85073509169

VL - 305

SP - S75-S85

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

SN - 0081-5438

IS - Suppl 1

ER -