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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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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Koçyiğit, Ç., Rujeerapaiboon, N. & Kuhn, D. Robust multidimensional pricing: separation without regret. Math. Program. (2021). https://doi.org/10.1007/s10107-021-01615-4
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