Optimal Design of Robust Combinatorial Mechanisms for Substitutable Goods

TL;DR

This paper develops a robust optimization approach for designing mechanisms to sell substitutable goods without prior preference information, aiming to minimize maximum regret in uncertain valuation scenarios.

Contribution

It introduces a robust optimization framework for multidimensional mechanism design with uncertain valuations, including a mixed-integer linear programming solution for revenue maximization.

Findings

Formulated a robust mechanism design model for substitutable goods.

Provided a mixed-integer linear programming method for revenue maximization.

Addressed valuation uncertainty without relying on prior preference distributions.

Abstract

In this paper we consider multidimensional mechanism design problem for selling discrete substitutable items to a group of buyers. Previous work on this problem mostly focus on stochastic description of valuations used by the seller. However, in certain applications, no prior information regarding buyers' preferences is known. To address this issue, we consider uncertain valuations and formulate the problem in a robust optimization framework: the objective is to minimize the maximum regret. For a special case of revenue-maximizing pricing problem we present a solution method based on mixed-integer linear programming formulation.