Auctioning Multiple Goods without Priors

TL;DR

This paper develops a mechanism design approach for selling multiple goods with minimal information, proposing a minimax regret mechanism using separate second-price auctions with random reserves to minimize worst-case regret.

Contribution

It introduces a novel minimax regret mechanism for multi-good auctions with limited information, specifically a separate second-price auction with random reserves.

Findings

Separate second-price auctions with random reserves are minimax regret mechanisms.

The approach minimizes worst-case expected regret across all value distributions.

The mechanism is effective under general upper bounds on bidders' values.

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.