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Stochastic game models of brand switching
Author(s) -
Laughland A.R.,
Nair K.P.K.
Publication year - 1974
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314694
Subject(s) - markov chain , game theory , minimax , product (mathematics) , value (mathematics) , sequential game , marketing , business , market share , advertising , microeconomics , mathematical economics , computer science , economics , mathematics , geometry , machine learning
In the study of the dynamic nature of brand switching, Markov chain theory has been used extensively. The conflicting interests of the companies involved have, however, not been explicitly incorporated. In this paper, two competing companies, each engaged in marketing a brand product, are considered. Brand switching by a consumer is influenced jointly but probabilistically by the two companies through their respective promotional actions and by the consumer's immediately preceding purchase. A stochastic game model is developed for determining the optimal promotional strategies of the companies, and the unique minimax value of the game in terms of market share. The structure of the model developed is that of a two‐person, zero‐sum, two‐state stochastic game. A method of solution and a few useful variations of the model are présentés. Practical interpretations of the solution are also included.