Optimal pricing of correlated product options under the paired combinatorial logit model

In this paper, we study price optimization with price-demand relationships captured by the paired combinatorial logit (PCL) model, which overcomes restrictions of the well-studied multinomial logit (MNL) and nested logit (NL) models. The PCL model allows for choice-correlation and, like the NL model, includes the MNL model as a special case. Compared to the NL models, the PCL model does not restrict the sequence of the choice structure and allows for different covariances among all pairs of choices. This additional flexibility in structure enables a more accurate representation of some choice settings and broadens its empirical applications. Hence, it is of both theoretical and practical interests to extend the normative studies on the MNL and NL models to the PCL model and examine the pricing problem under this model. Due to cross-nesting of choice alternatives, the pricing problem under the PCL model poses a greater challenge than the MNL and NL models. However, using the concept of P-matrix, we are able to identify conditions for a unique optimal price solution and develop an efficient and theoretically sound approach for finding the optimal prices. We show that the analysis and solution approach are generalizable to other GEV family models with cross-nested alternatives.