This paper presents a dynamic model of advertising in a duopoly and studies sales response to steady-state advertising policies. With steady-state advertising policies, sales levels must converge to one of a finite number of equilibria, and the equilibrium set consists of sinks and saddles with one more sink than saddle. When advertising is allowed to vary, the model may admit hysteresis; and we present an example which shows that accounting for word-of-mouth advertising can lead to hysteresis.
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Philip C. Jones (1983) studied this question.
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