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Robust multidimensional pricing: separation without regret

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Abstract

We study a robust monopoly pricing problem with a minimax regret objective, where a seller endeavors to sell multiple goods to a single buyer, only knowing that the buyer’s values for the goods range over a rectangular uncertainty set. We interpret this pricing problem as a zero-sum game between the seller, who chooses a selling mechanism, and a fictitious adversary or ‘nature’, who chooses the buyer’s values from within the uncertainty set. Using duality techniques rooted in robust optimization, we prove that this game admits a Nash equilibrium in mixed strategies that can be computed in closed form. The Nash strategy of the seller is a randomized posted price mechanism under which the goods are sold separately, while the Nash strategy of nature is a distribution on the uncertainty set under which the buyer’s values are comonotonic. We further show that the restriction of the pricing problem to deterministic mechanisms is solved by a deteministic posted price mechanism under which the goods are sold separately.

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Acknowledgements

This research was funded by the SNSF grant BSCGI0_157733 and by the NUS Start-up Grant R-266-000-131-133.

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Authors and Affiliations

  1. Luxembourg Centre for Logistics and Supply Chain Management, University of Luxembourg, Luxembourg City, Luxembourg

    Çağıl Koçyiğit

  2. Department of Industrial Systems Engineering and Management, National University of Singapore, Singapore, Singapore

    Napat Rujeerapaiboon

  3. Risk Analytics and Optimization Chair, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Daniel Kuhn

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  1. Çağıl Koçyiğit
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  2. Napat Rujeerapaiboon
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  3. Daniel Kuhn
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Correspondence to Çağıl Koçyiğit.

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Koçyiğit, Ç., Rujeerapaiboon, N. & Kuhn, D. Robust multidimensional pricing: separation without regret. Math. Program. 196, 841–874 (2022). https://doi.org/10.1007/s10107-021-01615-4

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