Robust Product-line Pricing under Generalized Extreme Value Models

TL;DR

This paper develops a robust pricing framework under GEV choice models, showing that optimal prices can be set with constant markups within certain conditions, and provides efficient methods to compute these prices.

Contribution

It introduces a robust optimization approach for product pricing under GEV models with uncertainty, deriving explicit formulas and convex optimization methods for practical computation.

Findings

Robust optimal prices have a constant markup under homogeneous price sensitivity.

Efficient convex optimization methods can compute the markup vector.

Numerical results demonstrate the robustness benefits against adverse scenarios.

Abstract

We study robust versions of pricing problems where customers choose products according to a generalized extreme value (GEV) choice model, and the choice parameters are not known exactly but lie in an uncertainty set. We show that, when the robust problem is unconstrained and the price sensitivity parameters are homogeneous, the robust optimal prices have a constant markup over products, and we provide formulas that allow to compute this constant markup by bisection. We further show that, in the case that the price sensitivity parameters are only homogeneous in each partition of the products, under the assumption that the choice probability generating function and the uncertainty set are partition-wise separable, a robust solution will have a constant markup in each subset, and this constant-markup vector can be found efficiently by convex optimization. We provide numerical results to illustrate the advantages of our robust approach in protecting from bad scenarios. Our results hold for convex and bounded uncertainty sets,} and for any arbitrary GEV model, including the multinomial logit, nested or cross-nested logit.