IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v131y2021ics0165188921001640.html
   My bibliography  Save this article

Advertising patterns in a dynamic oligopolistic growing market with decay

Author

Listed:
  • Amir, Rabah
  • Machowska, Dominika
  • Troege, Michael

Abstract

A finite-horizon Lanchester model of a (continuous-time) differential game of oligopolistic advertising is considered, and the analytical form of the unique closed-loop Nash equilibrium derived and analyzed. In contrast to previous research, the finite-horizon Lanchester model is modified to include two novel factors. First, a growing market allows us to analyze the competition for a potential market via generic advertising, with the latter giving the otherwise zero-sum-like game a public good dimension. Second, it is assumed that each firm’s market share declines in the absence of advertising efforts. The analysis investigates the Markovian (closed-loop) equilibrium calling for firms operating in a competitive growing market to invest in offensive, defensive or generic advertising in all or part of the decision horizon. In the most novel part of the paper, the non-cooperative outcome is compared to the Pareto-optimal or cooperative solution. The conclusions derived reveal significant differences in the resulting patterns of co-existence of the different dimensions of advertising over time, relative to the existing literature.

Suggested Citation

  • Amir, Rabah & Machowska, Dominika & Troege, Michael, 2021. "Advertising patterns in a dynamic oligopolistic growing market with decay," Journal of Economic Dynamics and Control, Elsevier, vol. 131(C).
    • Handle: RePEc:eee:dyncon:v:131:y:2021:i:c:s0165188921001640
    DOI: 10.1016/j.jedc.2021.104229
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165188921001640
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jedc.2021.104229?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Erickson, Gary M., 1995. "Differential game models of advertising competition," European Journal of Operational Research, Elsevier, vol. 83(3), pages 431-438, June.
    2. Wang, Qinan & Wu, Zhang, 2001. "A duopolistic model of dynamic competitive advertising," European Journal of Operational Research, Elsevier, vol. 128(1), pages 213-226, January.
    3. Amir, Rabah, 2000. "Modelling imperfectly appropriable R&D via spillovers," International Journal of Industrial Organization, Elsevier, vol. 18(7), pages 1013-1032, October.
    4. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    5. Gary M. Erickson, 1992. "Empirical Analysis of Closed-Loop Duopoly Advertising Strategies," Management Science, INFORMS, vol. 38(12), pages 1732-1749, December.
    6. Amir, Rabah, 1996. "Continuous Stochastic Games of Capital Accumulation with Convex Transitions," Games and Economic Behavior, Elsevier, vol. 15(2), pages 111-131, August.
    7. Samuel Sale, R. & Mesak, Hani I. & Inman, R. Anthony, 2017. "A dynamic marketing-operations interface model of new product updates," European Journal of Operational Research, Elsevier, vol. 257(1), pages 233-242.
    8. Michael P. Atkinson & Moshe Kress & Niall J. MacKay, 2021. "Targeting, Deployment, and Loss-Tolerance in Lanchester Engagements," Operations Research, INFORMS, vol. 69(1), pages 71-81, January.
    9. Léonard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521331586, January.
    10. Huang, Jian & Leng, Mingming & Liang, Liping, 2012. "Recent developments in dynamic advertising research," European Journal of Operational Research, Elsevier, vol. 220(3), pages 591-609.
    11. Kats, Amoz & Thisse, Jacques-Francois, 1992. "Unilaterally Competitive Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(3), pages 291-299.
    12. Kent D. Messer & Todd M. Schmit & Harry M. Kaiser, 2005. "Optimal Institutional Mechanisms for Funding Generic Advertising: An Experimental Analysis," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 87(4), pages 1046-1060.
    13. Sergei Savin & Christian Terwiesch, 2005. "Optimal Product Launch Times in a Duopoly: Balancing Life-Cycle Revenues with Product Cost," Operations Research, INFORMS, vol. 53(1), pages 26-47, February.
    14. AMIR, Rabah, 2001. "Stochastic games in economics and related fields: an overview," LIDAM Discussion Papers CORE 2001060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. Engelbert J. Dockner & Steffen Jørgensen, 2018. "Strategic Rivalry for Market Share: A Contest Theory Approach to Dynamic Advertising Competition," Dynamic Games and Applications, Springer, vol. 8(3), pages 468-489, September.
    16. M. Espinosa & Petr Mariel, 2001. "A model of optimal advertising expenditures in a dynamic duopoly," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 29(2), pages 135-161, June.
    17. Dung Nguyen & Lei Shi, 2006. "Competitive Advertising Strategies and Market-Size Dynamics: A Research Note on Theory and Evidence," Management Science, INFORMS, vol. 52(6), pages 965-973, June.
    18. Mark J. Roberts & Larry Samuelson, 1988. "An Empirical Analysis of Dynamic, Nonprice Competition in an Oligopolistic Industry," RAND Journal of Economics, The RAND Corporation, vol. 19(2), pages 200-220, Summer.
    19. David Soberman & Hubert Gatignon, 2005. "Research Issues at the Boundary of Competitive Dynamics and Market Evolution," Marketing Science, INFORMS, vol. 24(1), pages 165-174, September.
    20. Sung-Ha Hwang, 2017. "Conflict technology in cooperation: The group size paradox revisited," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 19(4), pages 875-898, August.
    21. Ruth N. Bolton, 1998. "A Dynamic Model of the Duration of the Customer's Relationship with a Continuous Service Provider: The Role of Satisfaction," Marketing Science, INFORMS, vol. 17(1), pages 45-65.
    22. Hwang, Sung-Ha & Rey-Bellet, Luc, 2020. "Strategic decompositions of normal form games: Zero-sum games and potential games," Games and Economic Behavior, Elsevier, vol. 122(C), pages 370-390.
    23. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, January.
    24. Marnik G. Dekimpe & Dominique M. Hanssens, 1995. "Empirical Generalizations About Market Evolution and Stationarity," Marketing Science, INFORMS, vol. 14(3_supplem), pages 109-121.
    25. Frank M. Bass & Anand Krishnamoorthy & Ashutosh Prasad & Suresh P. Sethi, 2005. "Generic and Brand Advertising Strategies in a Dynamic Duopoly," Marketing Science, INFORMS, vol. 24(4), pages 556-568, February.
    26. Rajshree Agarwal & Barry L. Bayus, 2002. "The Market Evolution and Sales Takeoff of Product Innovations," Management Science, INFORMS, vol. 48(8), pages 1024-1041, August.
    27. Sorger, Gerhard, 1989. "Competitive dynamic advertising : A modification of the Case game," Journal of Economic Dynamics and Control, Elsevier, vol. 13(1), pages 55-80, January.
    28. Marzieh Shahmarichatghieh & Arto Tolonen & Harri Haapasalo, 2015. "Product Life Cycle, Technology Life Cycle and Market Life Cycle: Similarities, Differences and Applications," Managing Intellectual Capital and Innovation for Sustainable and Inclusive Society: Managing Intellectual Capital and Innovation; Proceedings of the MakeLearn and TIIM Joint International Conference 2,, ToKnowPress.
    29. George E. Kimball, 1957. "Some Industrial Applications of Military Operations Research Methods," Operations Research, INFORMS, vol. 5(2), pages 201-204, April.
    30. Bagwell, Kyle, 2007. "The Economic Analysis of Advertising," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 28, pages 1701-1844, Elsevier.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kęstutis Peleckis, 2022. "Application of the Multicriteria Method Seeking to Assess Concentration, and Its Effects on Competition in the Manufacturing Sector," Sustainability, MDPI, vol. 14(19), pages 1-30, September.
    2. Kęstutis Peleckis, 2021. "Application of the DEMATEL Model for Assessing IT Sector’s Sustainability," Sustainability, MDPI, vol. 13(24), pages 1-14, December.
    3. Muhammad Irfan & Muhammad Shaukat Malik & Syeda Khadija Zubair, 2022. "Impact of Vlog Marketing on Consumer Travel Intent and Consumer Purchase Intent With the Moderating Role of Destination Image and Ease of Travel," SAGE Open, , vol. 12(2), pages 21582440221, May.
    4. Kęstutis Peleckis, 2022. "Determining the Level of Market Concentration in the Construction Sector—Case of Application of the HHI Index," Sustainability, MDPI, vol. 14(2), pages 1-16, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Huang, Jian & Leng, Mingming & Liang, Liping, 2012. "Recent developments in dynamic advertising research," European Journal of Operational Research, Elsevier, vol. 220(3), pages 591-609.
    2. Guidolin, Mariangela & Guseo, Renato, 2015. "Technological change in the U.S. music industry: Within-product, cross-product and churn effects between competing blockbusters," Technological Forecasting and Social Change, Elsevier, vol. 99(C), pages 35-46.
    3. Engelbert J. Dockner & Steffen Jørgensen, 2018. "Strategic Rivalry for Market Share: A Contest Theory Approach to Dynamic Advertising Competition," Dynamic Games and Applications, Springer, vol. 8(3), pages 468-489, September.
    4. Krishnamoorthy, Anand & Prasad, Ashutosh & Sethi, Suresh P., 2010. "Optimal pricing and advertising in a durable-good duopoly," European Journal of Operational Research, Elsevier, vol. 200(2), pages 486-497, January.
    5. Richards, Timothy J., 2002. "Dynamic Strategic Interaction: A Synthesis Of Modeling Methods," Western Economics Forum, Western Agricultural Economics Association, vol. 1(1), pages 1-5.
    6. A. Prasad & S. P. Sethi, 2004. "Competitive Advertising Under Uncertainty: A Stochastic Differential Game Approach," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 163-185, October.
    7. Chenavaz, Régis Y. & Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M., 2020. "Modeling the impact of product quality on dynamic pricing and advertising policies," European Journal of Operational Research, Elsevier, vol. 284(3), pages 990-1001.
    8. Lambertini, Luca & Zaccour, Georges, 2015. "Inverted-U aggregate investment curves in a dynamic game of advertising," Economics Letters, Elsevier, vol. 132(C), pages 34-38.
    9. Richards, Timothy J. & Patterson, Paul M., 2002. "Strategic Interaction With Multiple Tools: A New Empirical Model," Working Papers 28545, Arizona State University, Morrison School of Agribusiness and Resource Management.
    10. Gary M. Erickson, 2009. "Advertising Competition in a Dynamic Oligopoly with Multiple Brands," Operations Research, INFORMS, vol. 57(5), pages 1106-1113, October.
    11. Wang, Qinan & Wu, Zhang, 2001. "A duopolistic model of dynamic competitive advertising," European Journal of Operational Research, Elsevier, vol. 128(1), pages 213-226, January.
    12. Steffen Jørgensen & Simon-Pierre Sigué, 2015. "Defensive, Offensive, and Generic Advertising in a Lanchester Model with Market Growth," Dynamic Games and Applications, Springer, vol. 5(4), pages 523-539, December.
    13. Machowska Dominika, 2018. "Investigating the role of customer churn in the optimal allocation of offensive and defensive advertising: the case of the competitive growing market," Economics and Business Review, Sciendo, vol. 4(2), pages 3-23, June.
    14. Sylvie Tchumtchoua & Ronald W. Cotterill, 2010. "Optimal Brand and Generic Advertising Policies in a Dynamic Differentiated Product Oligopoly," Food Marketing Policy Center Research Reports 126, University of Connecticut, Department of Agricultural and Resource Economics, Charles J. Zwick Center for Food and Resource Policy.
    15. Erickson, Gary M., 2009. "An oligopoly model of dynamic advertising competition," European Journal of Operational Research, Elsevier, vol. 197(1), pages 374-388, August.
    16. Frank M. Bass & Anand Krishnamoorthy & Ashutosh Prasad & Suresh P. Sethi, 2005. "Generic and Brand Advertising Strategies in a Dynamic Duopoly," Marketing Science, INFORMS, vol. 24(4), pages 556-568, February.
    17. Laussel, Didier & Resende, Joana, 2014. "Dynamic price competition in aftermarkets with network effects," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 106-118.
    18. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2022. "A dynamic theory of spatial externalities," Games and Economic Behavior, Elsevier, vol. 132(C), pages 133-165.
    19. Fruchter, Gila E. & Kalish, Shlomo, 1998. "Dynamic promotional budgeting and media allocation," European Journal of Operational Research, Elsevier, vol. 111(1), pages 15-27, November.
    20. Alderighi, Marco & Bianchi, Carluccio & Lorenzini, Eleonora, 2016. "The impact of local food specialities on the decision to (re)visit a tourist destination: Market-expanding or business-stealing?," Tourism Management, Elsevier, vol. 57(C), pages 323-333.

    More about this item

    Keywords

    Dynamic oligopoly; Growing market; Market share decay; Lanchester model; Cooperative advertising;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:131:y:2021:i:c:s0165188921001640. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.