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Dynamic modeling of nontargeted and targeted advertising strategies in an oligopoly
Department of Computer Science, College of Charleston, Charleston, SC 29424, USA |
With the growing collection of sales and marketing data and depth of detailed knowledge of consumer habits and trends, firms are gaining the capability to discern customers of other firms from the potential market of uncommitted consumers. Firms with this capability will be able to implement a strategy where the advertising effort towards customers of competing firms may differ from that towards uncommitted consumers. In this work, dynamic models for advertising in an oligopoly setting with fixed total market size and sales decay are presented. Two models are described in detail: a nontargeted model in which the advertising effort is the same for both categories of prospective customers, and a targeted model that gives firms the capability to allocate effort across the two categories differently. In the differential game setting, open-loop and closed-loop Nash equilibrium strategies are derived for both models. Several strategic questions that a firm may face when practicing targeted advertising on a fixed budget are discussed and addressed.
References:
[1] |
F. M. Bass, A. Krishnamoorthy, A. Prasad and S.P. Sethi,
Advertising competition with market expansion for finite horizon firms, Journal of Industrial and Management Optimization, 1 (2005), 1-19.
doi: 10.3934/jimo.2005.1.1. |
[2] |
F. M. Bass, A. Krishnamoorthy, A. Prasad and S. P. Sethi,
Generic and brand advertising strategies in a dynamic duopoly, Marketing Science, 24 (2005), 556-568.
doi: 10.1287/mksc.1050.0119. |
[3] |
P. K. Chintagunta and N. J. Vilcassim,
An empirical investigation of advertising strategies in a dynamic duopoly, Management Science, 38 (1992), 1230-1244.
doi: 10.1287/mnsc.38.9.1230. |
[4] |
E. J. Dockner, S. Jørgensen, N. V. Long and G. Sorger,
Differential Games in Economics and Management Science, Cambridge University Press, 2000.
doi: 10.1017/CBO9780511805127. |
[5] |
D. Dragone, L. Lambertini and A. Palestini,
The Leitmann-Schmitendorf advertising game with $n$ players and time discounting, Applied Mathematics and Computation, 217 (2010), 1010-1016.
doi: 10.1016/j.amc.2010.02.031. |
[6] |
G. M. Erickson,
Differential game models of advertising competition, European Journal of Operational Research, 83 (1995), 431-438.
doi: 10.1016/0377-2217(94)00232-2. |
[7] |
G. Feichtinger,
The Nash solution of an advertising differential game: Generalization of a model by Leitmann and Schmitendorf, Automatic Control, IEEE Transactions on, 28 (1983), 1044-1048.
doi: 10.1109/TAC.1983.1103174. |
[8] |
G. E. Fruchter,
The many-player advertising game, Management Science, 45 (1999), 1609-1611.
doi: 10.1287/mnsc.45.11.1609. |
[9] |
G. E. Fruchter,
Oligopoly advertising strategies with market expansion, Optimal Control Applications and Methods, 20 (1999), 199-211.
doi: 10.1002/(SICI)1099-1514(199907/08)20:4<199::AID-OCA653>3.0.CO;2-M. |
[10] |
G. E. Fruchter,
Advertising in a competitive product line, Int. Game Theory Rev., 3 (2001), 301-314.
doi: 10.1142/S0219198901000439. |
[11] |
G. E. Fruchter and S. Kalish,
Closed-loop advertising strategies in a duopoly, Management Science, 43 (1997), 54-63.
doi: 10.1287/mnsc.43.1.54. |
[12] |
G. E. Fruchter and Z. J. Zhang, Dynamic targeted promotions a customer retention and acquisition perspective, Journal of Service Research, 7 (2004), 3-19. Google Scholar |
[13] |
R. F. Hartl and P. M. Kort, Advertising directed towards existing and new customers, in Optimal Control and Dynamic Games (eds. C. Deissenberg and R. Hartl), vol. 7 of Advances in Computational Management Science, Springer US, 2005, 3–18, URL http://dx.doi.org/10.1007/0-387-25805-1_1. Google Scholar |
[14] |
J. Huang, M. Leng and L. Liang,
Recent developments in dynamic advertising research, European Journal of Operational Research, 220 (2012), 591-609.
doi: 10.1016/j.ejor.2012.02.031. |
[15] |
R. Jarrar, G. Martín-Herrán and G. Zaccour,
Markov perfect equilibrium advertising strategies of lanchester duopoly model: A technical note, Management Science, 50 (2004), 995-1000.
doi: 10.1287/mnsc.1040.0249. |
[16] |
S. Jørgensen,
A survey of some differential games in advertising, Journal of Economic Dynamics and Control, 4 (1982), 341-369.
doi: 10.1016/0165-1889(82)90024-0. |
[17] |
S. Jørgensen, G. Martín-Herrán and G. Zaccour,
The Leitmann-Schmitendorf advertising differential game, Applied Mathematics and Computation, 217 (2010), 1110-1116.
doi: 10.1016/j.amc.2010.01.047. |
[18] |
S. Jørgensen and S.-P. Sigué, Defensive, offensive, and generic advertising in a lanchester model with market growth, Dynamic Games and Applications, 1–17, URL http://dx.doi.org/10.1007/s13235-015-0147-1.
doi: 10.1007/s13235-015-0147-1. |
[19] |
S. Jørgensen and G. Zaccour, Differential Games in Marketing, Springer, 2004. Google Scholar |
[20] |
G. E. Kimball,
Some industrial applications of military operations research methods, Operations Res., 5 (1957), 201-204.
doi: 10.1287/opre.5.2.201. |
[21] |
A. Krishnamoorthy, A. Prasad and S. P. Sethi,
Optimal pricing and advertising in a durable-good duopoly, European Journal of Operational Research, 200 (2010), 486-497.
doi: 10.1016/j.ejor.2009.01.003. |
[22] |
F. W. Lanchester, Aircraft in Warfare: The Dawn of the Fourth Arm, Appleton, New York, 1916. Google Scholar |
[23] |
G. Leitmann and W. Schmitendorf,
Profit maximization through advertising: a nonzero sum differential game approach, Automatic Control, IEEE Transactions on, 23 (1978), 645-650.
doi: 10.1109/TAC.1978.1101794. |
[24] |
D. Liu, S. Kumar and V. S. Mookerjee, Advertising strategies in electronic retailing: A differential games approach, Information Systems Research, 23 (2012), 903-917. Google Scholar |
[25] |
H. I. Mesak and A. F. Darrat, A competitive advertising model: Some theoretical and empirical results, The Journal of the Operational Research Society, 44 (1993), 491-502. Google Scholar |
[26] |
K. S. Moorthy, Competitive marketing strategies: Game-theoretic models, Handbooks in operations research and management science, 5 (1993), 143-190. Google Scholar |
[27] |
M. Nerlove and K. J. Arrow,
Optimal advertising policy under dynamic conditions, Economica, 29 (1962), 129-142.
doi: 10.1007/978-3-642-51565-1_54. |
[28] |
D. Nguyen and L. Shi,
Competitive advertising strategies and market-size dynamics: A research note on theory and evidence, Management Science, 52 (2006), 965-973.
doi: 10.1287/mnsc.1060.0509. |
[29] |
A. Prasad, S. P. Sethi and P. A. Naik,
Understanding the impact of churn in dynamic oligopoly markets, Automatica, 48 (2012), 2882-2887.
doi: 10.1016/j.automatica.2012.08.031. |
[30] |
J. Qi and D.-w. Wang,
Optimal control strategies for an advertising competing model, Systems Engineering -Theory & Practice, 27 (2007), 39-44.
doi: 10.1016/S1874-8651(08)60001-0. |
[31] |
S. P. Sethi,
Dynamic optimal control models in advertising: A survey, SIAM review, 19 (1977), 685-725.
doi: 10.1137/1019106. |
[32] |
M. L. Vidale and H. B. Wolfe,
An operations-research study of sales response to advertising, Operations Research, 5 (1957), 370-381.
doi: 10.1287/opre.5.3.370. |
[33] |
Q. Wang and Z. Wu,
A duopolistic model of dynamic competitive advertising, European Journal of Operational Research, 128 (2001), 213-226.
doi: 10.1016/S0377-2217(99)00346-X. |
show all references
References:
[1] |
F. M. Bass, A. Krishnamoorthy, A. Prasad and S.P. Sethi,
Advertising competition with market expansion for finite horizon firms, Journal of Industrial and Management Optimization, 1 (2005), 1-19.
doi: 10.3934/jimo.2005.1.1. |
[2] |
F. M. Bass, A. Krishnamoorthy, A. Prasad and S. P. Sethi,
Generic and brand advertising strategies in a dynamic duopoly, Marketing Science, 24 (2005), 556-568.
doi: 10.1287/mksc.1050.0119. |
[3] |
P. K. Chintagunta and N. J. Vilcassim,
An empirical investigation of advertising strategies in a dynamic duopoly, Management Science, 38 (1992), 1230-1244.
doi: 10.1287/mnsc.38.9.1230. |
[4] |
E. J. Dockner, S. Jørgensen, N. V. Long and G. Sorger,
Differential Games in Economics and Management Science, Cambridge University Press, 2000.
doi: 10.1017/CBO9780511805127. |
[5] |
D. Dragone, L. Lambertini and A. Palestini,
The Leitmann-Schmitendorf advertising game with $n$ players and time discounting, Applied Mathematics and Computation, 217 (2010), 1010-1016.
doi: 10.1016/j.amc.2010.02.031. |
[6] |
G. M. Erickson,
Differential game models of advertising competition, European Journal of Operational Research, 83 (1995), 431-438.
doi: 10.1016/0377-2217(94)00232-2. |
[7] |
G. Feichtinger,
The Nash solution of an advertising differential game: Generalization of a model by Leitmann and Schmitendorf, Automatic Control, IEEE Transactions on, 28 (1983), 1044-1048.
doi: 10.1109/TAC.1983.1103174. |
[8] |
G. E. Fruchter,
The many-player advertising game, Management Science, 45 (1999), 1609-1611.
doi: 10.1287/mnsc.45.11.1609. |
[9] |
G. E. Fruchter,
Oligopoly advertising strategies with market expansion, Optimal Control Applications and Methods, 20 (1999), 199-211.
doi: 10.1002/(SICI)1099-1514(199907/08)20:4<199::AID-OCA653>3.0.CO;2-M. |
[10] |
G. E. Fruchter,
Advertising in a competitive product line, Int. Game Theory Rev., 3 (2001), 301-314.
doi: 10.1142/S0219198901000439. |
[11] |
G. E. Fruchter and S. Kalish,
Closed-loop advertising strategies in a duopoly, Management Science, 43 (1997), 54-63.
doi: 10.1287/mnsc.43.1.54. |
[12] |
G. E. Fruchter and Z. J. Zhang, Dynamic targeted promotions a customer retention and acquisition perspective, Journal of Service Research, 7 (2004), 3-19. Google Scholar |
[13] |
R. F. Hartl and P. M. Kort, Advertising directed towards existing and new customers, in Optimal Control and Dynamic Games (eds. C. Deissenberg and R. Hartl), vol. 7 of Advances in Computational Management Science, Springer US, 2005, 3–18, URL http://dx.doi.org/10.1007/0-387-25805-1_1. Google Scholar |
[14] |
J. Huang, M. Leng and L. Liang,
Recent developments in dynamic advertising research, European Journal of Operational Research, 220 (2012), 591-609.
doi: 10.1016/j.ejor.2012.02.031. |
[15] |
R. Jarrar, G. Martín-Herrán and G. Zaccour,
Markov perfect equilibrium advertising strategies of lanchester duopoly model: A technical note, Management Science, 50 (2004), 995-1000.
doi: 10.1287/mnsc.1040.0249. |
[16] |
S. Jørgensen,
A survey of some differential games in advertising, Journal of Economic Dynamics and Control, 4 (1982), 341-369.
doi: 10.1016/0165-1889(82)90024-0. |
[17] |
S. Jørgensen, G. Martín-Herrán and G. Zaccour,
The Leitmann-Schmitendorf advertising differential game, Applied Mathematics and Computation, 217 (2010), 1110-1116.
doi: 10.1016/j.amc.2010.01.047. |
[18] |
S. Jørgensen and S.-P. Sigué, Defensive, offensive, and generic advertising in a lanchester model with market growth, Dynamic Games and Applications, 1–17, URL http://dx.doi.org/10.1007/s13235-015-0147-1.
doi: 10.1007/s13235-015-0147-1. |
[19] |
S. Jørgensen and G. Zaccour, Differential Games in Marketing, Springer, 2004. Google Scholar |
[20] |
G. E. Kimball,
Some industrial applications of military operations research methods, Operations Res., 5 (1957), 201-204.
doi: 10.1287/opre.5.2.201. |
[21] |
A. Krishnamoorthy, A. Prasad and S. P. Sethi,
Optimal pricing and advertising in a durable-good duopoly, European Journal of Operational Research, 200 (2010), 486-497.
doi: 10.1016/j.ejor.2009.01.003. |
[22] |
F. W. Lanchester, Aircraft in Warfare: The Dawn of the Fourth Arm, Appleton, New York, 1916. Google Scholar |
[23] |
G. Leitmann and W. Schmitendorf,
Profit maximization through advertising: a nonzero sum differential game approach, Automatic Control, IEEE Transactions on, 23 (1978), 645-650.
doi: 10.1109/TAC.1978.1101794. |
[24] |
D. Liu, S. Kumar and V. S. Mookerjee, Advertising strategies in electronic retailing: A differential games approach, Information Systems Research, 23 (2012), 903-917. Google Scholar |
[25] |
H. I. Mesak and A. F. Darrat, A competitive advertising model: Some theoretical and empirical results, The Journal of the Operational Research Society, 44 (1993), 491-502. Google Scholar |
[26] |
K. S. Moorthy, Competitive marketing strategies: Game-theoretic models, Handbooks in operations research and management science, 5 (1993), 143-190. Google Scholar |
[27] |
M. Nerlove and K. J. Arrow,
Optimal advertising policy under dynamic conditions, Economica, 29 (1962), 129-142.
doi: 10.1007/978-3-642-51565-1_54. |
[28] |
D. Nguyen and L. Shi,
Competitive advertising strategies and market-size dynamics: A research note on theory and evidence, Management Science, 52 (2006), 965-973.
doi: 10.1287/mnsc.1060.0509. |
[29] |
A. Prasad, S. P. Sethi and P. A. Naik,
Understanding the impact of churn in dynamic oligopoly markets, Automatica, 48 (2012), 2882-2887.
doi: 10.1016/j.automatica.2012.08.031. |
[30] |
J. Qi and D.-w. Wang,
Optimal control strategies for an advertising competing model, Systems Engineering -Theory & Practice, 27 (2007), 39-44.
doi: 10.1016/S1874-8651(08)60001-0. |
[31] |
S. P. Sethi,
Dynamic optimal control models in advertising: A survey, SIAM review, 19 (1977), 685-725.
doi: 10.1137/1019106. |
[32] |
M. L. Vidale and H. B. Wolfe,
An operations-research study of sales response to advertising, Operations Research, 5 (1957), 370-381.
doi: 10.1287/opre.5.3.370. |
[33] |
Q. Wang and Z. Wu,
A duopolistic model of dynamic competitive advertising, European Journal of Operational Research, 128 (2001), 213-226.
doi: 10.1016/S0377-2217(99)00346-X. |



[11] | [8] | [9] | [33] | [12] | [18] | This work | |
Model Type | Duo. | Oligo. | Oligo. | Duo. | Duo. | Duo. | Oligo. |
Sales Decay | No | No | No | Yes | No | No | Yes |
Effort To Market Potential | Yes | Yes | Yes | Yes | No | Yes | Yes |
Effort To Competitors' Customers | Yes | Yes | Yes | Yes | Yes | Yes | Yes |
Targeting | No | No | No | No | Yes | Yes | Yes |
Time Horizon | Infinite | Infinite | Infinite | Finite | Infinite | Finite | Finite |
Open-loop NE | Yes | Yes | Yes | Yes | Yes | No | Yes |
Closed-loop NE | Yes | Yes | Yes | Yes | Yes | Yes | Yes |
[11] | [8] | [9] | [33] | [12] | [18] | This work | |
Model Type | Duo. | Oligo. | Oligo. | Duo. | Duo. | Duo. | Oligo. |
Sales Decay | No | No | No | Yes | No | No | Yes |
Effort To Market Potential | Yes | Yes | Yes | Yes | No | Yes | Yes |
Effort To Competitors' Customers | Yes | Yes | Yes | Yes | Yes | Yes | Yes |
Targeting | No | No | No | No | Yes | Yes | Yes |
Time Horizon | Infinite | Infinite | Infinite | Finite | Infinite | Finite | Finite |
Open-loop NE | Yes | Yes | Yes | Yes | Yes | No | Yes |
Closed-loop NE | Yes | Yes | Yes | Yes | Yes | Yes | Yes |
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