E.V. Gromova, D.V. Gromov, Yu.E. Lakhina. On the solution of a differential game of managing the investments in an advertising campaign ... P. 64-75

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.

The paper was received by the Editorial Office on March 3, 2018.

Funding Agency:

Russian Science Foundation (Grant Number 17-11-01093).

Ekaterina Viktorovna Gromova, Dr. Phys.-Math. Sci., Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620990 Russia; Saint Petersburg University, St Peterburg, 199034 Russia, e-mail: e.v.gromova@spbu.ru.

Dmitrii Valer’evich Gromov, Cand. Technical Sci., Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620990 Russia; Saint Petersburg University, St Peterburg, 199034 Russia, e-mail: d.gromov@spbu.ru.

Yuliya Eduardovna Lakhina, undergraduate student, Saint Petersburg University, St Peterburg, 199034 Russia, e-mail: juliala1401@gmail.com.


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