In this note we prove that the class of valuation functions representable via integer assignment messages is a proper subset of strong substitutes valuations. Thus, there are strong substitutes valuations not expressible via assignment messages.
M. Bichler, M. Fichtl, S. Heidekrüger, N. Kohring, and P. Sutterer. Learning equilibria in symmetric auction games using artificial neural networks. Nature Machine Intelligence, 3:687–695, August 2021. [ DOI | link | pdf ] M. Bichler and S. Merting. Randomized scheduling mechanisms: Assigning course seats in a fair and efficient way. Production and Operations Management, 30(10):3540–3559, October 2021. [ DOI | link | pdf ] M. Bichler and S. Waldherr. Core-pricing in combinatorial exchanges with financially constrained buyers: Computational hardness and algorithmic solutions. Operations Research, 70(1):241–264, November 2021. [ DOI | pdf ] M. Bichler. Der Nobelpreis für Wirtschaftswissenschaften 2020 und seine Bezüge zum Operations Research. OR News, 69(3), 2020. [ link | pdf ] M. Bichler, M. Fichtl, and G. Schwarz. Walrasian equilibria from an optimization perspective: A guide to the literature. Naval Research Logistics, 68(4):496–513, 2020. [ DOI ] M. Bichler, V. Grimm, S. 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