  This work studies the parameter identification problem for the Markov chain
choice model of Blanchet, Gallego, and Goyal used in assortment planning. In
this model, the product selected by a customer is determined by a Markov chain
over the products, where the products in the offered assortment are absorbing
states. The underlying parameters of the model were previously shown to be
identifiable from the choice probabilities for the all-products assortment,
together with choice probabilities for assortments of all-but-one products.
Obtaining and estimating choice probabilities for such large assortments is not
desirable in many settings. The main result of this work is that the parameters
may be identified from assortments of sizes two and three, regardless of the
total number of products. The result is obtained via a simple and efficient
parameter recovery algorithm.
