Brand-Switching Markov Model

The brand-switching Markov model treats a consumer's sequence of brand purchases as a Markov chain, in which the probability of buying a given brand next depends only on the brand bought last. Its central object is the brand-to-brand transition matrix, whose rows record, for buyers of each brand, the probabilities of staying loyal or switching to each competitor on the next purchase occasion. Estimated from panel purchase histories by simple frequency counts, the matrix can be propagated forward to forecast how shares evolve and solved for its steady-state distribution to predict long-run equilibrium market shares. The diagonal of the matrix measures repeat-purchase loyalty while the off-diagonals measure switching, giving managers a structural picture of competitive churn. The model is the classic stochastic-choice representation of brand dynamics and a conceptual precursor to the loyalty variables used in scanner-panel logit models. It is most useful where purchases are frequent, the brand set is stable, and the first-order memory assumption is approximately satisfied.