A Quadratic Regularization for the Multi-Attribute Unit-Demand Envy-Free Pricing Problem - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

A Quadratic Regularization for the Multi-Attribute Unit-Demand Envy-Free Pricing Problem

(1, 2) , (2) , (2) , (1)
1
2
Quentin Jacquet
  • Function : Author
Wim van Ackooij
  • Function : Author
Clémence Alasseur
  • Function : Author
Stéphane Gaubert
  • Function : Author

Abstract

We consider a profit-maximizing model for pricing contracts as an extension of the unit-demand envy-free pricing problem: customers aim to choose a contract maximizing their utility based on a reservation price and multiple price coefficients (attributes). Classical approaches suppose that the customers have deterministic utilities; then, the response of each customer is highly sensitive to price since it concentrates on the best offer. To circumvent the intrinsic instability of deterministic models, we introduce a quadratically regularized model of customer's response, which leads to a quadratic program under complementarity constraints (QPCC). This provides an alternative to the classical logit approach, still allowing to robustify the model, while keeping a strong geometrical structure. In particular, we show that the customer's response is governed by a polyhedral complex, in which every polyhedral cell determines a set of contracts which is effectively chosen. Moreover, the deterministic model is recovered as a limit case of the regularized one. We exploit these geometrical properties to develop a pivoting heuristic, which we compare with implicit or non-linear methods from bilevel programming, showing the effectiveness of the approach. Throughout the paper, the electricity provider problem is our guideline, and we present a numerical study on this application case.

Dates and versions

hal-03504874 , version 1 (29-12-2021)

Identifiers

Cite

Quentin Jacquet, Wim van Ackooij, Clémence Alasseur, Stéphane Gaubert. A Quadratic Regularization for the Multi-Attribute Unit-Demand Envy-Free Pricing Problem. 2021. ⟨hal-03504874⟩
34 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More