# What are the benefits of a first price sealed bid auction?

All parties make a single bid. But do not disclose the bid to peers. The organizer chooses the maximum (or minimum) bid as the winner. What are benefits of such a system as opposed to normal auction where bidders openly declare the bids and keep updating based on the current maximum ( or minimum )?

A good article to read about this is by Susan Athey, Jonathan Levin and Enrique Seira. It has the title: "Comparing Open and Sealed Bid Auctions: Theory and Evidence from Timber Auctions," was published in the Quarterly Journal of Economics, vol. 126(1), 2011, 207-257, and is available online at:

The abstract includes this: "We study entry and bidding patterns in sealed bid and open auctions. Using data from U.S. Forest Service timber auctions, we document a set of systematic effects: sealed bid auctions attract more small bidders, shift the allocation towards these bidders, and can also generate higher revenue. A private value auction model with endogenous participation can account for these qualitative effects of auction format."

If there is a single item for sale, bidders are risk neutral, and bidders have independently and identically distributed private values then any two auctions that

• allocates the item to the highest value bidder in equilibrium
• offers the same surplus to the lowest value bidder

yield the same revenue (in expectation). This is the celebrated revenue equivalence theorem, which implies that first price sealed bid, second price sealed bid, English (open ascending), and Dutch (open descending) auctions all yield the same revenue. You can read a nice exposition of this theorem in the Appendix to Chapter 1 of Paul Klemperer's book Auctions: Theory and Practice (available here: http://www.nuff.ox.ac.uk/users/klemperer/VirtualBook/VBCrevisedv2.asp).

Some things that break this result:

If there is correlation between bidders private information then revenue equivalence breaks, and it is typically better (in expectation) to choose an auction format that reveals as much information as possible. This result, known as the Linkage Principle (originally due to Milgrom and Weber), implies that open ascending auctions earn more revenue in expectation than do sealed bid auctions.

If bidders are risk averse then the picture changes somewhat. In an open ascending auction, equilibrium bids remain unchanged (it's still optimal to stay in the bidding until your value is reached). A first price sealed bid auction, on the other hand, will tend to attract higher bids (roughly, if bidders are risk averse then they would prefer to pay more to reduce the chance of not winning the auction). So with risk averse bidders, one would expect the first price sealed bid auction to do better.

I higly recommend the entire first chapter of the Klemperer book linked above; it provides a nice, non-technical overview of the most important topics in auction theory research.

Let me add one more point in favor of the first-price auction. According to the definitions of Mohammad Akbarpour and Shengwu Li, it is the only mechanism that is both credible and static. Roughly speaking, credible means that, given the auction rules, the auctioneer cannot cheat by misrepresenting other bidders reports. For example, a second-price auction is not credible because the auctioneer could claim that the second-highest bid is just an $$\varepsilon$$ below the winning bid and thereby the price is raised. Read the full paper and slides here. This article is an easy read on the paper.

Just a partial answer. Your post combines several questions into one. First, why a sealed-bid auction at all? Second, why a first-price instead of some other type of sealed-bid auction? (There is also the question of whether you are interested in theory or practice.)

For the second question, in theory, the equilibria of a first-price auction seem more robust than those of a second-price auction. In a second-price or ascending-bid auction, a threat to bid very highly, even if not credible, can discourage participation (especially if the other bidders don't know it's not credible). However, every equilibrium in a first-price auction has good welfare and good revenue (I can provide some references on this if you like). So some people like the first-price in theory for this reason.

• Yes, please do add some references, I'd be interested to read them Feb 25 '15 at 6:25
• @EnergyNumbers, I am mainly thinking of this paper: arxiv.org/abs/1404.5943, but I think the ideas are now in a more readable format in Hartline's book Mechanism Design and Approximation, in the new "Chapter X", Theorem X.1 and Corollary X.17.
– usul
Feb 25 '15 at 13:21