The Milgrom Assignment Auction represents the next generation of multi-product auctions. It can accept bids to buy, sell, swap, or any combination of these; it can deal with anywhere from just a few bidders and items to thousands of both; and, once initiated, it is instantaneous.

Auctionomics’ software is based on Milgrom’s innovations in game theory, and built around a proprietary “messaging technology” that enables bidders, using just a few keystrokes, to express not only supply- or demand-curves for each product, but also substitution possibilities among different products. This ability to give a sophisticated picture of its preferences eliminates the clock-auction bidder’s need to sit around waiting to express its demand at various prices.

Our innovative message space is the key to our software’s unique combination of power and flexibility, allowing it to retain the information-revealing advantages of the clock auction, while bringing the extreme speed and ease of use of the sealed-bid format to a host of new applications.

As a sealed-bid auction, the Milgrom Assignment Auction runs itself, calculating the value-maximizing allocation and market clearing prices without the need for multiple rounds. This immediacy and efficiency is especially important when speed is paramount, for example when time to run the auction is short, or when bidders are dispersed in multiple time zones around the world.

The Milgrom Assignment Auction also has enhancements that are not available in clock auctions. One allows bidders to express budget constraints that are respected in the bidding for multiple items. Another allows buyers or sellers to name minimum quantities. A third allows bidders to explicitly account for fixed costs. None of these enhancements can be added to a standard clock auction.

The immediacy of any sealed-bid auction incurs a cost: a single round precludes the gradual emergence, over the course of the auction, of useful information about the depth of demand or supply. But no sealed-bid format has ever before allowed bidders the flexibility offered by the Milgrom Assignment Auction.

The basic Milgrom Assignment Auction guarantees these powerful results:

  • Quantities are always optimal for all bidders: every bidder gets exactly what it wants, given the quoted prices.
  • Markets clear exactly: supply is set equal to demand for every product.

Unless its specified constraints prevent it, every bidder is assigned the combination of items that give it the highest margin, and every bidder thus trades every item that offers it a positive margin according to its bid: each bidder sells all its goods that offer it a positive “seller’s margin” (the difference between the market-clearing price and the bidder’s minimum selling-price), and each also purchases all goods that offer it a positive “buyer’s margin” (the difference between market-clearing price and the bidder’s maximum buying-price).

The Milgrom Assignment Auction can also be run as a two-stage auction: while avoiding the ad hoc adjustments common in clock auctions, and maintaining the incremental accuracy necessary to avoid overshooting equilibrium, the two-stage version offers the information-feedback advantages of the clock auction while running much faster.

The table below compares the features of clock auctions, traditional sealed-bid auctions, and the Milgrom Assignment Auction:

  Milgrom Assignment Traditional Sealed Bids Clock Auctions
Adapted to multiple products Yes Yes Yes
Easy to use with simple substitutions Yes No No
Allow general expression of substitutes Yes No Yes
Finishes Instantly Yes Yes No
Finds Exact Market Clearing Prices Yes Yes No
Support Swaps Yes No No