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A Generalization of the Nerlove-Arrow Model to Multi-Firms Advertising under Uncertainty

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  • Charles S. Tapiero

    (Hebrew University)

Abstract

This paper considers a multi-firms advertising model under uncertainty of the Nerlove-Arrow type. It is shown (under a Markovian assumption of the advertising process) that the probability of sales for a firm in a multi-firms setting is given by a Poisson distribution with a parameter given by its market share at a given time. Using the multi-firms model developed in this paper, advertising differential games are resolved. In particular, a two-firms advertising model with concave advertising costs is used to obtain optimum advertising budgets for competitive firms.

Suggested Citation

  • Charles S. Tapiero, 1979. "A Generalization of the Nerlove-Arrow Model to Multi-Firms Advertising under Uncertainty," Management Science, INFORMS, vol. 25(9), pages 907-915, September.
    • Handle: RePEc:inm:ormnsc:v:25:y:1979:i:9:p:907-915
    DOI: 10.1287/mnsc.25.9.907
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    Cited by:

    1. Chenavaz, Régis Y. & Eynan, Amit, 2021. "Advertising, goodwill, and the Veblen effect," European Journal of Operational Research, Elsevier, vol. 289(2), pages 676-682.
    2. Erickson, Gary M., 1995. "Differential game models of advertising competition," European Journal of Operational Research, Elsevier, vol. 83(3), pages 431-438, June.
    3. Tapiero, Charles S., 2000. "The NBD repeat purchase process and M/G/[infinity] queues," International Journal of Production Economics, Elsevier, vol. 63(2), pages 141-145, January.
    4. Chan, Tat Y. & Narasimhan, Chakravarthi & Yoon, Yeujun, 2017. "Advertising and price competition in a manufacturer-retailer channel," International Journal of Research in Marketing, Elsevier, vol. 34(3), pages 694-716.
    5. Du, Rong & Hu, Qiying & Ai, Shizhong, 2007. "Stochastic optimal budget decision for advertising considering uncertain sales responses," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1042-1054, December.
    6. Luca Grosset & Bruno Viscolani, 2004. "Advertising for a new product introduction: A stochastic approach," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 149-167, June.

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