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Robust Multidimensional Pricing: Separation without Regret

ağıl Koyiğit (cagil.kocyigit***at***epfl.ch)
Napat Rujeerapaiboon (isenapa***at***nus.edu.sg)
Daniel Kuhn (daniel.kuhn***at***epfl.ch)

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.

Keywords: robust optimization, pricing, mechanism design, regret minimization

Category 1: Robust Optimization

Citation: 07/2018

Download: [PDF]

Entry Submitted: 07/24/2018
Entry Accepted: 07/26/2018
Entry Last Modified: 03/26/2020

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