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A birth–death model of advertising and pricing

Published online by Cambridge University Press:  01 July 2016

S. Christian Albright  and
Wayne Winston
S. Christian Albright*
Affiliation:
Indiana University School of Business
Wayne Winston
Affiliation:
Indiana University School of Business
*
∗Postal address: Indiana University, Graduate School of Business, School of Business Building, Bloomington, IN47401, U.S.A.
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Abstract

This paper employs the methods currently used to solve many queuing control models in order to investigate the behavior of a firm's optimal advertising and pricing strategies over time. Given that a firm's market position expands or deteriorates in a probabilistic way which depends upon the current position, the rate of advertising, and the price the firm charges, we present conditions which ensure that the optimal level of advertising is a monotonic function of the firm's market position, and we discuss the economic meaning of these conditions. Furthermore, although the primary focus is upon a non-competitive environment, we develop the above model as a non-zero sum, two-person stochastic game and show that an equilibrium strategy exists which is simple to compute.

Keywords

BIRTH–DEATH PROCESSMARKOV DECISION MODELMONOTONE OPTIONAL POLICIES
Type
Research Article
Information
Advances in Applied Probability , Volume 11 , Issue 1 , March 1979 , pp. 134 - 152
Copyright
Copyright © Applied Probability Trust 1979 

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