Equilibrium Stochastic Choice and Market Penetration Theories: Derivations and Comparisons

We show in this paper the formal connection between brand switching models and multiperiod analysis of brand choice behavior. A formal, well-defined stochastic process is developed from stochastic choice premises which permits analysis of any event or combination of events in terms of subsets of the market. The formal connection between single-brand analysis and multi-brand analysis is demonstrated. The parameters of the stochastic process involve the market shares and a measure of the heterogeneity of the population. This information is sufficient to permit the estimation of aggregate brand switching on adjacent trials or brand penetration and multiple brand purchasing over sequences of purchase occasions.