Two Models of Brand Switching

It is well known that brand choice can be described by a Markov chain. In order to put some structure into the transition probabilities we model brand choice as a two-stage decision process: (1) whether to continue or whether to reconsider the last choice, (2) in the latter case which brand to choose. A distinction must then be made as to whether the last brand is ruled out (hypothesis II) or not (hypothesis I) giving rise to two different probability models. In the case of only two brands, the transition probabilities can always be modelled in either way.The following problems are considered. How to test the existence of choice probabilities? How in the ergodic case the state probabilities, i.e., the long-run market shares are determined? What are the implications of zero-one probabilities of retention or choice? Under what conditions are market shares equalized? It is also suggested that the retention probabilities depend on product attributes while the choice probabilities respond to advertising.