A dynamic oligopoly marketing model of advertising

Lihong Shi ; Ovanes Petrosian

Contributions to game theory and management, Tome 11 (2018), pp. 207-223.

Résumé

We consider a dynamic oligopoly advertising model for both noncooperative and cooperative setting. Feedback Nash equilibrium strategies and cooperative strategies are found to determine the optimal advertising efforts of each firm for both setting respectively. Besides, depending upon the cooperative strategies, imputation is introduced as an optimal allocation of joint payoff and Imputation Distribution Procedure is used to guarantee the time consistency for cooperation.

Détail

Keywords: advertising competition, optimal control, dynamic programming, time consistency.

Bibliographie

[1] Bellman R., Dynamic Programming, Princeton University Press, Princeton, NJ, 1957 | MR | Zbl

[2] Basar T., Olsder G. J., Dynamic noncooperative game theory, Classics in Applied Mathematics, 23, 2nd edition, SIAM, Philadelphia, 1999 | MR | Zbl

[3] Yeung D. W. K., “On Differential Games with a Feedback Nash Equilibrium”, Journal of Optimization Theory and Applications, 82:1 (1994), 181–188 | DOI | MR | Zbl

[4] Yeung D. W. K., Petrosyan L. A., Subgame-consistent Economic Optimization, Springer, New York, 2012 | MR

[5] Erickson G. M., Dynamic Models of Advertising Competition, 2 ed., Kluwer, Norwell, MA, 2003

[6] Nash J. F. Jr., “Equilibrium points in n-person games”, Proceedings of the National Academy of Sciences, 36:1 (1950), 48–49 | DOI | MR | Zbl

[7] Nash J. F. Jr., “Non-cooperative games”, Annals of Mathematics, 54:2 (1951), 286–295 | DOI | MR | Zbl

[8] Petrosyan L. A., Danilov N. N., “Stability of solutions in non-zero sum differential games with transferable payoffs”, Vestnik Leningrad State University, 1 (1979), 52–59 | MR | Zbl

[9] Petrosyan L. A., Yeung D. W. K., “Dynamically stable solutions in randomly-furcating differential games”, Proceedings of the Steklov Institute of Mathematics, 253 (2006), 208–220 | DOI | MR

[10] Petrosjan L. A., “Strongly time-consistent differential optimality principles”, Vestnik St. Petersburg University, Mathematics, 26 (1993), 40–46 | MR

[11] Petrosyan L. A., “Time-consistency of solutions in multi-player differential games”, Vestnik Leningrad State University, 4 (1977), 46–52 | Zbl

[12] Petrosyan L. A., Yeung D. W. K., Subgame Consistent Economic Optimization, Birkhäuser Boston Incorporated, 2012 | MR | Zbl

[13] Naik P. A., Prasad A., Sethi S. P., “Building brand awareness in dynamic oligopoly markets”, Management Science, 54:1 (2008), 129–138 | DOI | Zbl

[14] Chander P., Tulkens H., “A core-theoretic solution for the design of cooperative agreements on transfrontier pollution”, International Tax and Public Finance, 2:2 (1995), 279–293 | DOI

[15] Prasad A., Sethi S. P., Naik P. A., “Optimal control of an oligopoly model of advertising”, INCOM 2009 (Moscow, Russia, 2009)

[16] Prasad A., Sethi S. P., “Competitive advertising under uncertainty: A stochastic differential game approach”, Journal of Optimization Theory and Applications, 123:1 (2004), 163–185 | DOI | MR | Zbl

[17] Sorger G., “Competitive dynamic advertising: A modification of the Case game”, Journal of Economic Dynamics and Control, 13:1 (1989), 55–80 | DOI | MR | Zbl

[18] Shapley L. S., “A Value for N-Person Games”, Contributions to the Theory of Games II, eds. Kuhn W., Tucker A. W., Princeton Univ. Press, Princeton, 1953, 307–317 | MR

[19] Jorgensen S., Zaccour G., Differential Games in Marketing, Kluwer, Academic Publishers, Boston, MA, 2004

[20] Jorgensen S., Yeung D. W. K., “Inter- and intragenerational renewable resource extraction”, Annals of Operations Research, 88 (1999), 275–289 | DOI | MR | Zbl

[21] Jorgensen S., Martin-Herran G., Zaccour G., “Agreeability and Time Consistency in Linear-State Differential Games”, Journal of Optimization Theory and Applications, 119 (2003), 49–63 | DOI | MR | Zbl

[22] Basar T., Olsder G. J., Dynamic Noncooperative Game Theory, Academic Press, London, 1995 | MR | Zbl