First-price procurement auctions can be highly inefficient without limits
At What Cost? (In)efficiency in First-Price Procurement Auctions
Computer Science and Game Theory
Summary
This paper studies how efficient first-price procurement auctions are when bidders compete by offering the lowest price to provide a service or goods. The authors found that without restrictions, the auction’s outcome can be very inefficient, with costs much higher than the best possible. They show that limiting bid ranges or adding a fake “phantom” bid can improve efficiency, but only up to a point. No method based solely on the known cost range can get rid of inefficiency dependence on the cost variability.
What this means in practice
- •For auction designers: Design first-price procurement auctions with bid limits or phantom bidders to reduce inefficiency in bidder competition.
- •For public procurement officials: Improve purchasing processes by understanding how bid restrictions affect cost efficiency in competitive contracting auctions.
A theory result. No direct application yet.
Authors
Simone Palazzotto, Andrés Cristi
Abstract
We study the efficiency of Bayes-Nash equilibria in first-price procurement auctions. We measure efficiency by the Price of Anarchy (PoA): the ratio between the expected social cost in equilibrium and the minimum expected social cost resulting from a socially optimal allocation. We first show that the standard first-price procurement auction has no bounded PoA guarantee. We construct equilibria in which every bidder is indifferent between all bids in a common interval, so that bids can be arbitrarily large, and the PoA is unbounded. If costs lie in an interval $[\underline c,\bar c]$ but bids are not restricted, the PoA equals the trivial ratio $\bar c/\underline c$. We hence study ways to restore a finite guarantee, first by characterizing the PoA when bids lie in $[\underline c,\bar c]$, which leads to the tight bound $1 + \frac1{e^2}(\frac{\bar c}{\underline c}-1)$. Alternatively, we introduce the notion of a phantom bidder: the auctioneer accepts the lowest bid only if it does not exceed a phantom bid, drawn independently of the costs, and otherwise buys from an outside option at cost $\bar c$. We show that a simple fixed phantom bid, i.e., a deterministic cap, gives PoA $=\frac1e\sqrt {\frac{\bar c}{\underline c}}+O(1)$. We further show that no phantom mechanism whose construction depends only on the cost interval, under a mild regularity condition, whatever distribution it uses and whatever it reveals about the phantom bid before bidding, can improve on the $\sqrt{\frac{\bar c}{\underline c}}$ dependence.