Have you ever bought or sold something on eBay? If yes, were you thinking that you were participating in an auction?

Most people, when thinking about auctions, imagine a room where bidders keep raising their stakes to buy a painting, an antique, real estate, or something else that the market struggles to assign a price to, until the auctioneer declares the object sold. Well, auctions may be more present in your everyday life than you think. For example, every time you enter a search query on the Internet, an automated auction takes place and determines the ads that appear on the page. A considerable market that billed Google Advertising Revenue $224.47 billion last year. Therefore, understanding the mechanism that regulates auctions today can be an essential part of grasping further facets of economics.

There are multiple types of auctions and the design of the auction you are participating in determines the bids you will play. According to economic theory, the four “standard” formats are the first price-sealed bid auction, the second price-sealed bid auction, the ascending auction (English auction), and the descending auction.

Rules of the game

At this point, you may be asking yourself “ok, but why do we need different game designs?”. The answer is that details play a key role in the realization of a Nash Equilibrium. The idea of Nash Equilibrium is a very simple one: in a game, each player best responds to the other player’s best response. The crucial assumption is that players’ beliefs about the opponent’s bidding behavior are always correct. Each game may have more than one Nash Equilibria, but it is impossible to determine which of them will actually take place. In fact, a multiplicity of Nash equilibria as well as departures from the standard assumption of correct beliefs will be the core of our discussion. Think of a common English auction, like one that you may have watched on TV for the selling of an art painting, where prices go up and the last man standing pays the price at which the second last dropped out; you will soon realize that concepts like ‘correct belief’ or ‘best response’ seem quite distant. How often could a bidder accurately predict how much the other bidders value the painting? Is it always the case that a bidder can assign a monetary value to his personal art taste? Precisely because predictability and certainty are not features of this world, how the game is played makes a big difference. Rules are one certain thing in life, they are then crucial in the realization of an auction’s outcome. In fact, auctions may be ascending or descending, and they may prescribe a limited number of prices available to bidders. If a bidder exploits well her first-mover advantage, she may well influence the price updating during the game.

Among other structural features of auctions, the most influential element on the outcome is information symmetry among players. In many cases, each bidder has some information that is not observable to others. We should now seek to understand how bidders value the objects they are bargaining for. Since participants generally have different goals and act strategically, the behavior of one bidder cannot be understood in isolation from that of other bidders. Private information settings (each bidder’s evaluation yields no information regarding other bidders’ evaluations) are generally rare. Instead, we will focus our attention on common-value models developed by Wilson, which assume that bidders have the same ex-post evaluation of the object for sale but different ex-ante private evaluations.

In the mineral-rights model developed by Wilson (1969), ex-post evaluations are interdependent, and bidders update their own private values according to Bayesian thinking (i.e., they integrate private values with additional information from signals of other bidders). In the presence of interdependencies, a bidder is likely to learn something from other bidders’ estimates. Hence, he may want to revise his own bid accordingly. Wilson brings the example of an oil-lease auction where companies bid for the extraction of oil in a given unexplored geographical area. How much oil can be extracted is a common matter of uncertainty to all bidders. Even though, each of them may hire an appraisal to perform a geological test. If a bidder knows the other bidder’s test results, she will likely revise her evaluation. Economically speaking we may translate the latter by saying that a higher common value implies higher signals which are conditionally independent of the common value. Therefore, under Bayesian Nesh Equilibria in this model, the winner, who is also the most optimistic bidder, is likely to have overestimated the true value; a phenomenon known as the winner’s curse.

Multi-object auctions

So far, we have been discussing auctions in which a single object is sold, but real-world auctions have increasingly been used to sell multiple objects at the same time. Nowadays, thanks to the development of computerized auctions, the number of transactions which can take place simultaneously has been growing exponentially. The most interesting application of multi-object auctions involves on one hand, divisible objects such as government debt and electricity, on the other hand heterogeneous, interrelated objects like Spectrum licenses. Although, it is important to stress that the distinction is not always so clear. Consider for example the case of electricity, which is homogeneous and finely divisible at its source, but the cost of delivery may vary according to the location. In the first place, we will discuss share auctions, used to sell divisible objects, and secondly, we will examine auctions for interrelated objects, like Spectrum auctions which involve exceptionally large values.  

Auctions for divisible objects

Under share auctions (Wilson 1979), bidders receive fractional shares of the item at a sale price that equates to the demand and supply of shares. Each bidder compiles a schedule which assigns prices to varying fractional shares of the item, that is a bid is equivalent to a demand schedule. The seller then selects the price such that the total of the shares requested by all the bidders matches the available supply of shares. In real terms, the bidder can confuse the opponents by ‘shading’ her bids below her true value. The intuition is simple: when seeking to purchase multiple units, a bidder knows that the price she offers for marginal units may affect the price that she pays for inframarginal units. Thus, bidding through demand schedules in a share auction scenario allows bidders to gain an additional move. Not only that, but the large variety of possible strategies also generates several equilibria on which bidders can sometimes coordinate, yielding low profits for the seller.

Despite the difficulties outlined above, the goal of well-functioning auction formats would be to reach a unique Pareto efficient equilibrium. In the late 1980s, these issues were addressed through a general model of competition with a supply-function setting that reversed the roles of bidders from buyers to sellers. At that time, procurement auctions with supply-function bids became increasingly important as several countries privatized their energy market. Even though supply-function models are still affected by a multiplicity of equilibria, innovations like sufficiently discrete bidding functions (bid caps) as well as other features proper of the energy market (uncertainty, capacity constraints…) proved to be effective in the potential realization of a unique equilibrium outcome. For what concerns bid shading instead, the data outline degrees of shading to be positively correlated with participants’ market shares. In the context of electricity markets, the markup seems to grow large as capacity becomes a binding constraint.

Another modern application of share auctions is used for the allocation of greenhouse gas emissions allowances. In July 2021, the European Commission introduced an auctioning system for the selling of carbon emissions allowances to make polluters pay for negative externalities, with the aim of reaching climate neutrality by 2050. A strategy which prescribes a net 55% reduction in greenhouse gas emissions by 2030. The EU Emissions Trading System stated a series of criteria according to which auctions must guarantee predictability, cost-efficiency, and simultaneous access to relevant information . An interesting feature in the context of the European common market is that auctioning is gradually replacing free allocation for allowances in all EU ETS sectors, except aviation. According to the European authorities, this mechanism best ensures the efficiency, transparency, and simplicity of the system. Not to mention the creation of large incentives for investment in a low-carbon economy.

Auctions for interrelated objects

Before moving to auctions for interrelated objects, we should clarify one last detail. When talking about divisible objects, we have introduced the solution (share auctions) before the potential problem (carbon emissions). But while, in a share auction, we treat each fractional unit as equivalent to the other (precisely, shares of a unique item at the sale: a ‘unitized’ allowance), this type of division may not fit all the markets. In the context of interrelated objects, bidders are not interested in the quantity they obtain, rather they are much more interested in how their gain can improve what they already have. In poor terms, they act more as stamp collectors. The reason for reversing the solution-problem logic lies in the fact that, before introducing Spectrum auctions, regulators failed to grasp this bidders’ behavior.

In the early 1990s, a huge demand for mobile communication made the US government decide to use auctions to allocate radio-spectrum licenses among telecommunication firms. In the years anticipating the technological revolution, the Federal Communications Commission (FCC) used to apply the so-called ‘command and control’ attitude by relying on lotteries or administrative procedures (‘beauty contests’) to sell licenses. Regulation determined spectrum uses and users. Spectrum usage rights were narrow and limited only to specific uses, like broadcasting or satellite. Moreover, the FCC used to specify the location of services based on a point, not an area. Consequently, the geography of the country was not exhaustively licensed, making the service in many areas unavailable. Later, the introduction of cellular devices in 1984 required a larger coverage of the spectrum and a more flexible licensing structure.

The main argument for using auctions reflects two types of efficiency concerns: first, assigning the objects to the most productive supplier saves on secondary markets for reassignments. Secondly, raising funds through markets rather than taxation avoids costly tax distortions. Besides generating higher short-run revenues for the government, the trivial goal is one to chase a long-run perspective of higher revenues and higher welfare in a more competitive market. In fact, one of the sources of distortions in the telecommunication market is that bidders generally prefer combinations of complementary licenses. Licenses are generally purchased in blocks, thus the providers’ optimal strategy to dominate a market is to collect spectrum allocations in neighboring geographical areas.

Under this regime, governments face a challenging trade-off between rising revenues and allocating the spectrum efficiently. However, both auctions and lotteries have failed to pursue the government interest and the best format that would allow governments to maximize social welfare is still to be found. In light of the considerations drawn above, the SMRA (Simultaneous Multiple Rounds Auction) model is deemed to be an effective mechanism to overlook both the interests of buyers and sellers.

Spectrum allocation and the SMRA

The SMRA format developed by Milgrom and Wilson, Nobel laureates in 2020, allows bidders to place bids on an arbitrary number of objects over multiple rounds. Multi-round designs have the additional advantage that they allow each bidder to learn which objects are likely to be relevant, decreasing information asymmetries and the winner’s curse. At the first round, prices are set sufficiently low that all objects are in excess demand: in each round, bidders raise their bids by an integer number of increments on any object they are interested in. At the end of each round, a ‘provisional winner’ is declared. Bidding closes only when excess demand is exhausted, and the provisional winner gets his objects and pays the bids. In 1994, the FCC raised $20 billion for the US federal government, which attracted considerable attention from other countries. As a result, the SMRA auction format has become the dominant design for spectrum sales worldwide.

One major drawback of the model is known as the exposure problem. In fact, most bidders in spectrum auctions are looking for complementary objects, that is, they tend to purchase licenses in blocks to dominate markets that are geographically close by. Hence, when playing more than one stage, the risk of not winning all of them is very high because of optimal allocations.

A new challenge for public policy

It is worth saying that auctions are one of the most antique ways of selling. And, at the same time, one of the most modern as their use has been recently on a crescendo. A new frontier wide open to innovation attracts the interest of many scholars on the line of pioneering work by Milgrom and Wilson. Not only because of their ability to achieve significant efficiency in government revenues and welfare allocation but also because of their ability to make multiple buyers interact at the same time. In a globalized world, like the one we live in, transactions on a global scale are a daily matter. Auctions work well with this scope because they provide a transparent and effective solution to the modern problems of public policy on a wide range of needs. A scale that shifts from market privatizations to public allowances.


https://www.nobelprize.org/uploads/2020/09/advanced-economicsciencesprize2020.pdf  – “Improvements to auction theory and Invention of new auction formats”, The Royal Swedish Academy of Sciences, 12 October 2020

https://www.fcc.gov/news-events/podcast/going-once-going-infinitely – “How the FCC went from ‘beauty contests’ to spectrum auctions.”, FCC, 19 January 2021

https://climate.ec.europa.eu/eu-action/eu-emissions-trading-system-eu-ets/auctioning_en#auctioning-rules – EU Emission Trading System, Climate Action and Auctioning

https://www.jstor.org/stable/1884475?seq=13 – “Auctions of Shares”, The Quarterly Journal of Economics, Robert Wilson, November 1979