Customer Behavior As a Markov Process

Abstract

Simple Markov processes appear to provide a fruitful conceptual basis for study of customer populations in the face of marketing activity. The purpose of this paper is to summarize characteristics and some implications and applications of the Markov model. Characteristic behavior of the model is compared with published data, and areas for further analytical and experimental effort are indicated.

A birth–death model of advertising and pricing

“…Define V(i,! )a and V(i)a to be the analogues of V(i, 11') 13 and V(i)13 for a continuous-time Markov decision process in which the discount rate is a. For the case T = 00, Lippman's Theorem 1 from [17] yields the following results.…”

“…Then a policy 7T is (3-optimal if V(i, 1T)13 = V(i)13 for each i. We also define V n (i) 13 to be the maximum expected discounted reward that can be earned by operating the process for n periods. The following results follow from Theorem 1 of [17].…”

“…Beginning with the seminal work of Vidale and Wolfe [33] many researchers (see [1], [25], [26], [30], and [31]) have utilized optimal control theory in an attempt to determine how a firm should advertise so as to maximize the discounted present value of sales minus advertising expenditures. Although there is a vast literature in which a firm's market position evolves in a stochastic manner (see [12], [13], [15], [20], [30], and [31]) most of this work (with exception of [30] and [31]) does not allow the firm to vary its advertising expenditure. Even Tapiero's work ( [30] and [31]) has drawbacks in that it requires very difficult computations and it provides little insight into the form of the optimal policy.…”

An Investigation of Brand Choice Processes

“…Amongst the first of these were Herniter and Magee (1961). They gave an exposition of the theory of Markov chains and showed some possible applications to the brand choice process.…”

Markovian decision processes with uncertain rewards

“…However, the Markov process is mathematically tractable and is often a satisfactory assumption when modeling a physical system. Examples are found in many areas including inventory control (8), production planning (14), equipment replacement (13) .md Marketing (10).…”