Selling Multiple Complements with Packaging Costs

TL;DR

This paper introduces a novel framework for package assignment with multiple indivisible items, using incremental costs and graph-based interdependence to characterize Walrasian equilibrium prices and ensure fair, transparent pricing.

Contribution

It develops a linear programming approach to characterize equilibrium prices and provides conditions for their existence via ascending auctions, incorporating preferences over package partitions.

Findings

Equilibrium prices are uniform, anonymous, and linear in packages.

Prices and marginal gains have a nested structure, with a closed-form characterization for complete graphs.

Sufficient conditions for package-linear competitive prices are established with auction implementation.

Abstract

We consider a package assignment problem with multiple units of indivisible items. The seller can specify preferences over partitions of their supply between buyers as packaging costs. We propose incremental costs together with a graph that defines cost interdependence to express these preferences. This facilitates the use of linear programming to characterize Walrasian equilibrium prices. Firstly, we show that equilibrium prices are uniform, anonymous, and linear in packages. Prices and marginal gains exhibit a nested structure, which we characterize in closed form for complete graphs. Secondly, we provide sufficient conditions for the existence of package-linear competitive prices using an ascending auction implementation. Our framework of partition preferences ensures fair and transparent dual pricing and admits preferences over the concentration of allocated bundles in the market.