Author:
Rilwan Jewaidu, ,Kumam Poom,Ahmed Idris, , , ,
Abstract
<abstract><p>In this paper, advertising competition among $ m $ firms is studied in a discrete-time dynamic game framework. Firms maximize the present value of their profits which depends on their advertising strategy and their market share. The evolution of market shares is determined by the firms' advertising activities. By employing the concept of the discrete-time potential games of González-Sánchez and Hernández-Lerma (2013), we derived an explicit formula for the Nash equilibrium (NE) of the game and obtained conditions for which the NE is an overtaking optimal. Moreover, we analyze the asymptotic behavior of the overtaking NE where the convergence towards a unique steady state (turnpike) is established.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference33 articles.
1. V. M. Adukov, N. V. Adukova, K. N. Kudryavtsev, On a discrete model of optimal advertising, J. Comput. Eng. Math., 2 (2015), 13–24.
2. S. M. Aseev, M. I. Krastanov, V. M. Veliov, Optimality conditions for discrete-time optimal control on infinite horizon, Pure Applied Funct. Anal., 2 (2017), 395–409.
3. A. O. Belyakov, On a sufficient condition for infinite horizon optimal control problems, 2019. Available from: https://arXiv.org/abs/1909.07379.
4. W. A. Brock, On existence of weakly maximal programmes in a multi-sector economy, Rev. Econ. Stud., 37 (1970), 275–280.
5. W. A. Brock, Differential games with active and passive variables, In: Mathematical economics and game theory, Springer, 1977. doi: 10.1007/978-3-642-45494-3_4.