Technical note - Pricing under the nested attraction model with a multistage choice structure

We develop a solution approach to the centralized pricing problem of a nested attraction model with a multistage tree structure. We identify conditions under which the optimal solution can be uniquely determined, and we characterize the optimal solution as a fixed point of a single variable. In the special case of a multistage nested logit model, we show the impact of asymmetry in price sensitivity and adjustment index (also known as the dissimilarity index) and we derive a closed-form solution when the tree structure is symmetric. Many existing results in the literature regarding the single or two-stage nested attraction model are shown to be special cases of the results we have derived. We show that the equal markup property, which holds for the single-stage logit model with symmetric price sensitivity, in general does not hold for products that do not share the same immediate parent node in the nested choice structure even when price sensitivities are the same for all products.