Dynamic Models of Advertising Competition: Open- and by Gary M. Erickson

By Gary M. Erickson

For years, i've been inspired by way of how dynamic markets are. advertising and marketing recommendations are not often winning with no alterations through the years, and advertising and marketing managers want continuously to observe, and expect while attainable, very important alterations within the advertising atmosphere, for you to adapt their advertising techniques to altering marketplace stipulations. It moves me as vital that the dynamic components of selling be modeled and studied, and an important a part of my examine task has been devoted to exploring the character and implications of dynamic advertising ideas. the promoting box has used quite a few types and methodologies within the try to comprehend dynamic markets. i have to thank my dissertation consultant, Dave Montgomery at Stanford, for initially turning my consciousness towards time-varying parameter versions a few 14 years in the past. From that plat­ shape, i've got proceeded to look for versions that catch the essence of dynamic advertising, in addition to for methodological instruments, empirical in addition to analytical, that permit insightful examine of such models.

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DYNAMIC MODELS OF ADVERTISING COMPETITION Previous studies modeling advertising competition Study Model type Solution type Analysis method Mukundan and Elsner (1975) Vidale- Wolfe Open-loop, linear feedback Numerical Deal (1979) Vidale- Wolfe Open-loop Numerical Case (1979) Lanchester Vi dale- Wolfe/ Lanchester Perfect Analytical Open-loop= closed-loop Analytical Feichtinger (1983) Vidale-Wolfe/ Lanchester Open-loop= closed-loop Qualitative Olsder (1976) Excess advertising Open-loop= closed-loop Analytical J 0rgensen ( 1982b) Excess advertising Open-loop Analytical Feichtinger and Dockner (1984) Excess advertising Open-loop Qualitative Deal, Sethi, and Thompson (1979) Vi dale- Wolfe/ excess advertising Open-loop Numerical Sorger(1989) Lanchester I excess advertising Open-loop, feedback Qualitative Erickson ( 1985) Lanchester Open-loop Analytical, numerical Teng and Thompson (1983) Diffusion Open-loop Numerical Horsky and Mate (1988) Diffusion Closed-loop Numerical Dockner and J0rgensen (1990) Tapiero (1979) Diffusion Open-loop Analytical Nerlove- Arrow Open-loop, linear feedback Qualitative Fershtman (1984) Nerlove- Arrow Open-loop Analytical Rao (1984) Nerlove- Arrow Open-loop Analytical Thepot (1983) Friedman (1983) Nerlove- Arrow Qualitative Nerlove- Arrow Open-loop Open-loop Fershtman, Mahajan, and Muller (1990) Nerlove- Arrow Open-loop Analytical Leitmann and Schmitendorf (1978) Analytical ANALYTICAL MODELS AND STRATEGY CONCEPTS 33 the findings.

As a consequence, we should not be surprised if closed-loop equilibrium strategies turn out to be quite different than open-loop strategies. 4), and identify value functions V 1(M), V2 (M) according to V((M) = kt V2(M) = kz. > A2(M, V(, V2) = (-a2~2V2M) 11 o-a 2 > = At(M) = A1(M). 17) where c 1, c2 are arbitrary constants. 16). Instead, however, we will examine an equivalent system of equations not involving the value functions. 16) for VI , V2 (and dropping the asterisks on the advertising functions), VI(M) = A:-a'(M) Ut~t(1 - M) V2(M) -A~-a2(M).

For these models, closed-loop equilibria are in general different from open-loop strategies, although, as will be shown through examples, it is possible to find closedloop strategies that resemble open-loop strategies, dynamically. We will restrict each model to involve a duopoly (two competitors) and a single state variable, to avoid partial differential equations. The Lanchester model has been advanced as an attractive model that directly incorportes both competition and the dynamic nature of markets (Little 1979).

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