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Selling Multiple Complements with Packaging Costs

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  • Simon Finster

    (FAIRPLAY - IA coopérative : équité, vie privée, incitations - CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - GENES - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - GENES - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique - IP Paris - Institut Polytechnique de Paris - Criteo AI Lab - Criteo [Paris] - Centre Inria de l'Institut Polytechnique de Paris - Centre Inria de Saclay - Inria - Institut National de Recherche en Informatique et en Automatique, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - GENES - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - GENES - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Simon Finster, 2025. "Selling Multiple Complements with Packaging Costs," Post-Print hal-05233957, HAL.
    • Handle: RePEc:hal:journl:hal-05233957
    DOI: 10.1145/3736252.3742522
    Note: View the original document on HAL open archive server: https://hal.science/hal-05233957v1
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    References listed on IDEAS

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    1. Stoneham, Gary & Chaudhri, Vivek & Ha, Arthur & Strappazzon, Loris, 2003. "Auctions for conservation contracts: an empirical examination of Victoria’s BushTender trial," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 47(4), pages 1-24.
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