Ordinal Structure in Multi-Unit Auctions

Massachusetts Institute Of Technology, Cambridge MA

Investigators

Abstract

The research project will contribute to the basic theory of auctions of multiple identical objects (``multi-unit auctions"). The focus of the project is on establishing ``monotonicity" of equilibria in such auctions, i.e. that bids are non-decreasing functions of the bidder's private information. Efforts to establish monotonicity using standard approaches have stalled for the most part in general environments of interest, but this research brings to bear promising new tools from lattice theory. Existing research has applied such tools to prove existence of monotone equilibrium in a limited model of one-sided multi-unit auctions. This project aims to develop that approach further to apply to large auctions with many buyers and sellers in more general environments. Since monotonicity is a crucial ingredient for efficiency, such research may lead to new results proving asymptotic efficiency of equilibria in uniform-price auctions. Multi-unit auctions provide a compelling ``micro-foundation" for markets with many buyers and sellers. Multi-unit auction theory also models important real-world auctions such as U.S. Treasury bond issue and regional electricity procurement auctions. Unfortunately, the basic theory of such auctions is quite incomplete. Worse yet, the existing single-object auction theory provides an unreliable guide for understanding multi-unit auctions. This research will clarify fundamental properties of bidding behavior in multi-unit auctions and leverage its basic theory contributions to re-address the fundamental and age-old question: ``When can we expect markets to efficiently allocate resources?"