ByAdam M. Zaretsky
In 1994, the Federal Communications Commission (FCC) began auctioning electromagnetic spectrum bandwidth to firms interested in using it for personal communications services (PCS). Before that time, spectrum bandwidth had been given away to broadcasters through administrative hearings or lotteries—procedures that were not only inefficient, but also costly. According to the Commerce Department, the federal government in the 1980s gave away cellular phone licenses valued at $46 billion.1 Realizing the revenue potential, Congress turned to auctions as a way to both allocate spectrum more efficiently than it had in the past and to reap revenue that could be used to help offset the budget deficit. Economists were called upon to aid in the design and implementation of these auctions, which have proven quite successful.
In a word, auctions are better at allocating spectrum than administrative hearings or lotteries because auctions enable market forces to designate who will receive how much of the resource. As with all other resources in the economy, there is a limited amount of spectrum bandwidth; thus, scarcity exists. And like other scarce goods and services in the economy, prices are the best allocator.2
But unlike many other goods in the economy, which are abundantly available and frequently purchased, spectrum bandwidth is difficult to price because, until 1994, it hadn't been sold before. Auctions overcome the pricing problem through their bidding mechanisms, which let potential buyers reveal their individual values of an item. Moreover, because sellers can set the rules of the selling process and announce them upfront, all auction participants know exactly what is expected of themselves and others. In other words, auctions are orderly, organized mechanisms through which market-clearing prices can be determined.
In many ways, bidding for an item at an auction is a lot like playing poker. With each hand, a player has to decide whether to call, raise or fold. He bases this decision on two factors: the cards in his own hand and his best guess as to the cards in the other players' hands. At the same time, he must also try to figure out how the other players might react to his decisions. The understanding and explanation of this behavior is called game theory.
Game theory examines the strategic interaction and decision-making behavior of players in a game, accounting for what they know, what they think others know, and how they think others will act on this knowledge. A well-known example of the theory is the simple two-person game called the Prisoners' Dilemma. In this game, Bud and Lou commit a crime. Although there is little evidence against them, they are still arrested. The two are separated and told their options. If both confess, each will get four years in prison. If neither confesses, each will be charged with a lesser crime and get a two-year sentence. But if, for instance, Bud cooperates and rats on Lou, who says nothing, Bud will get one year, while Lou will get eight. If Lou rats on Bud, and Bud keeps quiet, the sentences will be reversed.
What should Bud and Lou do? The best option would be for them to agree not to confess so both can get off with only two years in prison. But this strategy requires Bud and Lou to collude and trust each other to uphold their end of the bargain. The trust is tested, though, once the two are separated.
If Bud truly believes that Lou will keep quiet, he can cut his sentence from two years to one by taking the deal and confessing. If Lou is thinking exactly the same thing, though, both will end up confessing and, therefore, each will get four years.
As the accompanying table shows, Bud's best strategy is actually to confess irrespective of which strategy Lou chooses (confessing or keeping quiet).3 Why? Because if Lou chooses to confess, Bud's options are either to also confess and serve four years, or to keep quiet and serve eight. If Lou chooses to keep quiet, then Bud's options are either to confess and serve one year, or to also keep quiet and serve two. The choice is obvious: Always confess. In this game, confessing is the dominant strategy because it prevails over all other choices. Neither player becomes better off by switching strategies and keeping quiet.
|Lou's Strategies||Confess||Bud: 4 years
Lou: 4 years
|Bud: 8 years
Lou: 1 year
|Keep Quiet||Bud: 1 year
Lou: 8 years
|Bud: 2 years
Lou: 2 years
Game theory, then, models players' best responses to opponents' actions, assuming that each player always acts in his own best interest. The models also assume that any action taken by a player is the best strategy available, given the anticipated action of his opponent.
Understanding this type of strategic interaction was important for the FCC because it needed to know how bidders would behave during the spectrum auction. Moreover, the commission also needed to design a set of auction rules that would accomplish Congress' goals. Therefore, the FCC called upon game theorists to aid in the design of the auction rules, giving economists a chance to test their theories in a real-world setting.
Every auction suffers from a number of potential problems. By defining a proper set of rules for all participants to follow, however, such problems can be minimized. For example, a common problem in an English auction—in which an auctioneer invites oral bids until the last bid made goes unchallenged—is that participants can collude, thereby reducing the final price of the item. Agreements can be made beforehand, determining who will win and at what price. Cheating (breaking the agreement) is checked because others in the pact will see it occur.
A simple solution to collusion is to hold an auction in which all participants submit sealed, written bids, and the highest bid wins. With sealed bids, effective collusion cannot occur because breaking the pact is now easy. This type of auction, however, can lead to the winner's curse—a situation in which a winning bidder pays more for an item than he thinks it's worth because he has no information about what others might think it's worth. If bidders are aware of this possibility, they might lower their offers, thereby reducing the seller's revenue.
To avoid the winner's curse, a Vickrey auction—a sealed-bid auction in which the highest bidder wins, but pays the amount of the second-highest bid—could be used.4 This type of auction eliminates the winner's curse because bidders are now motivated to reveal their true valuations of the item at hand through their bids. Why? If a player bids less than his valuation, he risks losing the item; if he bids more, however, he may end up paying too much. The player's incentive, therefore, is to bid his valuation.
In practice, however, Vickrey auctions don't always go as planned. In 1990, for example, a New Zealand firm that bid NZ$100,000 for spectrum ended up paying the second-highest bid, NZ$6. And in another case, a firm that bid NZ$7 million paid NZ$5,000. These situations occurred because New Zealand's government failed to require a minimum bid. Not surprisingly, the government has since amended its auction rules.
The FCC had to plan for other considerations as well: for instance, the likelihood that firms bidding on spectrum would want to aggregate licenses in certain areas. In other words, the company bidding on the Los Angeles license would most likely also want to own the licenses for the city's surrounding communities because of economies of scale. If the firm could not secure the Los Angeles license, the other licenses would be worth less to it, prompting the firm to reduce its bid and, hence, the government's revenue. With this in mind, the FCC decided to auction all licenses simultaneously in multiple rounds, enabling firms both to aggregate as they chose and to withdraw from regions in which bids were getting too large.5 Auctions end when no new bids are submitted for any license on the block.
The proof of game theory's success is in the pudding. By carefully designing rules to avoid the potential pitfalls of auctions, economists have helped the FCC raise more than $23 billion since 1994, far exceeding the $10 billion in revenue the Office of Management and Budget had originally projected.6 But this success needn't be limited to spectrum or the FCC. Oil and mineral rights, foreclosed homes, and even landing rights at airports are just a few examples of other potential candidates for auctions. And if the overall success enjoyed by the FCC can be repeated in some of these other areas, the potential economic gains to everyone could truly be large.
Binmore, Ken. Fun and Games: A Text on Game Theory (Lexington, Mass.: D.C. Heath and Company, 1992).
McAfee, R. Preston, and John McMillan. "Analyzing the Airwaves Auction," Journal of Economic Perspectives (Winter 1996), pp. 159-75.
McMillan, John. "Selling Spectrum Rights," Journal of Economic Perspectives (Summer 1994), pp. 145-62.
________. "Why Auction the Spectrum?" Telecommunications Policy 19:3 (1995), pp. 191-99.
"Revenge of the Nerds," The Economist (July 23, 1994), p. 70.
U.S. Department of Commerce. U.S. Spectrum Management Policy: Agenda for the Future. Washington, D.C., NTIA Special Publication 91-23 (February 1991).
Zaretsky, Adam M. "Rush-Hour Horrors: How Economics Tackles Congestion," The Regional Economist, Federal Reserve Bank of St. Louis (April 1997), pp. 10-11.