Auctioning Multiple Goods without Priors

Wanchang Zhang

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arXiv · 2204.13726

Auctioning Multiple Goods without Priors

Wanchang Zhang

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Abstract

I consider a mechanism design problem of selling multiple goods to multiple bidders when the designer has minimal amount of information. I assume that the designer only knows the upper bounds of bidders' values for each good and has no additional distributional information. The designer takes a minimax regret approach. The expected regret from a mechanism given a joint distribution over value profiles and an equilibrium is defined as the difference between the full surplus and the expected revenue. The designer seeks a mechanism, referred to as a minimax regret mechanism, that minimizes her worst-case expected regret across all possible joint distributions over value profiles and all equilibria. I find that a separate second-price auction with random reserves is a minimax regret mechanism for general upper bounds. Under this mechanism, the designer holds a separate auction for each good; the formats of these auctions are second-price auctions with random reserves.

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Wanchang Zhang. 2022-04-28. Auctioning Multiple Goods without Priors. https://arxiv.org/abs/2204.13726

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