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Advertising Events in a Competitive Framework

Author

Listed:
  • L. Grosset

    (Dipartimento di Matematica Pura e Applicata)

  • B. Viscolani

    (Dipartimento di Matematica Pura e Applicata)

Abstract

We study the problem of how to minimize the advertising costs for a one-time entertainment event taking competition into account. Using the concept of Nerlove-Arrow goodwill, we describe a market where two single players organize two different events. A single-player instance of the same problem has been analyzed already in the literature using both the Nerlove-Arrow dynamics and the Bass dynamics, but without considering a competitive framework. In this work, starting from a linear-quadratic model, we consider competition in the market and we study the problem in the settings of linear-quadratic deterministic and stochastic differential games. The analytical tractability of the problem allows us to characterize the Nash equilibria and to study the new features of the competitive scenario. In the deterministic instance of the model, we show that competition decreases efficiency. On the other hand, when the goodwill evolution is stochastic, competition may even increase efficiency by a diversification effect.

Suggested Citation

  • L. Grosset & B. Viscolani, 2010. "Advertising Events in a Competitive Framework," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 375-385, August.
    • Handle: RePEc:spr:joptap:v:146:y:2010:i:2:d:10.1007_s10957-010-9648-7
    DOI: 10.1007/s10957-010-9648-7
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    References listed on IDEAS

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    1. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    2. Alessandra Buratto & Luca Grosset, 2006. "A communication mix for an event planning: a linear quadratic approach," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 14(3), pages 247-259, September.
    3. Gustav Feichtinger & Richard F. Hartl & Suresh P. Sethi, 1994. "Dynamic Optimal Control Models in Advertising: Recent Developments," Management Science, INFORMS, vol. 40(2), pages 195-226, February.
    4. 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, September.
    5. Jørgensen, Steffen & Kort, Peter M. & Zaccour, Georges, 2009. "Optimal pricing and advertising policies for an entertainment event," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 583-596, March.
    6. Marinelli, Carlo, 2007. "The stochastic goodwill problem," European Journal of Operational Research, Elsevier, vol. 176(1), pages 389-404, January.
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