Bidding in Multi-Unit Auctions under Limited Information

TL;DR

This paper analyzes multi-unit auctions with limited bidder information, characterizing optimal bids that minimize worst-case expected utility loss, and compares outcomes across auction formats.

Contribution

It introduces a method to compute optimal prior-free bids in multi-unit auctions with multi-dimensional private info, including closed-form solutions in some cases.

Findings

Optimal prior-free bids minimize maximal expected utility loss.

Minimax-loss bids are unique in pay-as-bid auctions.

Comparison of auction formats yields testable predictions.

Abstract

We study multi-unit auctions in which bidders have limited knowledge of opponent strategies and values. We characterize optimal prior-free bids; these bids minimize the maximal loss in expected utility resulting from uncertainty surrounding opponent behavior. Optimal bids are readily computable despite bidders having multi-dimensional private information, and in certain cases admit closed-form solutions. In the pay-as-bid auction the minimax-loss bid is unique; in the uniform-price auction the minimax-loss bid is unique if the bidder is allowed to determine the quantities for which they bid, as in many practical applications. We compare minimax-loss bids and auction outcomes across auction formats, and derive testable predictions.