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Robust multidimensional pricing: separation without regret.
- Source :
-
Mathematical Programming . Nov2022, Vol. 196 Issue 1/2, p841-874. 34p. - Publication Year :
- 2022
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *PRICES
*ZERO sum games
*NASH equilibrium
*ROBUST optimization
Subjects
Details
- Language :
- English
- ISSN :
- 00255610
- Volume :
- 196
- Issue :
- 1/2
- Database :
- Academic Search Index
- Journal :
- Mathematical Programming
- Publication Type :
- Academic Journal
- Accession number :
- 160073109
- Full Text :
- https://doi.org/10.1007/s10107-021-01615-4