Optimal Auction Through Deep Learning
This post reviews auction theory and the paper Optimal Auction Through Deep Learning. https://arxiv.org/abs/1706.03459
Since I have never studied economics, there are limits to how deeply I can discuss auction theory itself. In this first post, I would like to briefly explore auctions, why auction theory earned a Nobel Prize, and how it can be applied.
Auctions: A difficult mathematical puzzle
Auctions are a familiar form of trade. Buyers compete by raising their offers for an item, whether it is a guitar on eBay, services on MyHammer, or artwork at a traditional auction house. Yet studying the detailed rules turns this familiar transaction into a highly complex research problem. Stanford economists Robert Wilson and Paul Milgrom illustrate that complexity: their understanding of auction rules and their development of improved formats earned them the joint 2020 Nobel Prize in Economic Sciences.
Even the simplest auctions are difficult to analyze within game theory, which mathematically examines problems involved in decision-making. Work by William Vickrey and John Harsanyi in the 1960s helped establish auction analysis within economic theory; they later received Nobel Prizes in 1996 and 1994, respectively. Building on this work, Wilson and his student Milgrom developed influential theories explaining how auctions take shape in different economic settings. Their research helps us understand bidder behavior and evaluate auction rules. It is increasingly relevant as digitization makes auctions more complex across the economy: mobile spectrum, fishing rights, online markets, energy markets, and industrial procurement are just a few examples.
Spectrum auctions
Public interest in auctions grew in the 1990s, when governments worldwide sought ways to allocate wireless broadband spectrum through auctions. Mobile operators saw substantial business opportunities, while governments saw an opportunity to raise considerable revenue and select the companies best equipped to manage the spectrum. A stronger business model should support a higher bid for a license. Governments also wanted allocations spread across several companies rather than allowing one operator to monopolize the network. Technical constraints complicated matters, since not every combination of frequencies was feasible.
Choosing operators was therefore a multifaceted problem: which rules would select the best bidders, assign technically feasible combinations of frequencies, and maximize public revenue? Milgrom and Wilson advised governments and developed sophisticated rules, while other scholars advised companies on bidding strategies. Their proposals rested on a strong theoretical foundation. One important contribution was recognizing that bidders partly rely on shared underlying information when deciding their bids. If one bidder values a license highly, others are also likely to do so. The seller therefore wants to identify the bidder with the best business model, or the one able to generate the greatest profit at the lowest cost. In principle, that bidder should offer the highest price.
But the highest bidder might simply have overestimated the license's value rather than having the best business model. It could win and later realize it had paid too much—the 'winner's curse.' Milgrom and Wilson showed how rational bidders account for that danger, entering with limits designed to avoid regretting a win. This helps explain the benefits of an open auction. Each time a competitor drops out, remaining bidders learn more about how others value the license. That additional information can sometimes justify a more confident bid.
Developing simultaneous multiple-round auctions
An open auction for a single license cannot capture all these benefits. Mobile operators often need a portfolio of licenses to offer an attractive service—for instance, coverage across several regions. It is hard to value one license without knowing which others will be available. This creates a need to auction multiple licenses simultaneously.
On the basis of this research, Milgrom and Wilson developed a new format: an open process in which spectrum licenses for several regions are auctioned simultaneously over multiple rounds. This is the simultaneous multiple-round auction. Carefully designed rules allow information initially held by individual bidders to come together gradually during the auction. That reduces the risk of ending up with an unwanted combination of licenses or suffering the winner's curse. Higher expected auction revenue also benefits the seller.
Milgrom and Wilson's idea has greatly influenced spectrum auctions around the world. More fundamentally, their work laid foundations applicable to countless auctions throughout everyday life. The 2020 Nobel Prize illustrates how closely elegant mathematical models in basic research can connect with practical applications in economics.