Game theory in action: designing the US airwaves auction

In 1993 the US Congress decided to auction off licences to use the electromagnetic spectrum for personal communication services. This involved selling off thousands of licences with different geographic coverage and at different spectrum locations.

Auctioning off the licences was a break with the tradition of direct licence allocation to those with a bigger 'need'. It required the Federal Communications Commission (FCC) to set up a mechanism capable of efficiently allocating licences to the bidder most valuing it. Game theory (and game theorists) played an important role in both the design of the actual auction mechanism used and in advising bidders on optimal bidding strategies.

Auctions are, a priori, an ideal method for allocating goods to those who place a higher value on them, as these people are likely to make the highest bid. However, research by game theorists has shown that the design of the auction matters, both for the efficiency of the allocation - does the good go to the person who values it most? - and the revenues earned for the seller. In this particular instance, Congress had asked the FCC to ensure that the spectrum was used in an efficient and intensive way, rather than simply to maximise auction income for the Federal government.

According to an account in the Journal of Economics Perspectives, by two of the economists involved in the design (Preston McAfee of Texas A & M and John McMillan of University of California, San Diego), the designers considered the existence of complementarities between the licences as the most important threat to efficiency in this particular context.

For the bidder, the value of each individual licence depends to a large extent on whether another licence has been obtained so that several licences can be grouped together to form a coherent region. The auction design needed to allow for the coherent aggregation of licences, so that a bidder would not find himself bidding for a licence as a part of a whole to discover that he is in fact awarded an incoherent entity of much smaller value to him or her.

Following the advice of several economic theorists employed by the bidders, including Stanford economists Paul Milgrom and Robert Wilson, plus McAfee and McMillan, the FCC opted for a novel design: a simultaneous ascending auction, in which the bidding for all the licences remained open as long as bidding in any of the licences remained active. The aggregation of licences was facilitated by the fact that bidding and the observation of the bids, were simultaneous.

For all its advantages, the simultaneous ascending auctions involved an important risk of implicit collusion between rival bidders. To avoid this problem, the identity of the bidder would remain hidden until the auction concluded. But it was still possible for a bidder to find ways to signal their intention in order to ensure allocation of the preferred licence at a low cost. In fact, as subsequent portions of the spectrum were auctioned off, complaints about this type of behaviour increased. For example, Mercury PCS, a US telecom operator, was accused of highlighting its interest in winning a specific licence by ending the bid amount in January 1997 with the postal codes of the particular city in which it was interested.

On the bidders' side, the consultants to the bidders have not made public their recommendations. We can only speculate that game theory was used by bidders both to enhance the rationality of their bidding and to understand and influence the bidding behaviour of the rival bidders.

First, game theory could introduce a higher degree of rationality in the bidding process by helping to design optimal bidding strategies. For example, game theorists have long understood that in auction settings bidding as much as one would be actually willing to pay for a good could lead to what is known as the winner's curse: imagine that a licence will be in fact equally valuable to any firm, but that each firm has a different opinion about how valuable it is likely to be. Clearly the winning bid is most likely to be from the most optimistic firm. But the most optimistic firm's estimate of the value of the audio waves will be biased upwards - it will be too high. In fact, if the highest bidder wins without taking into account this effect, he will overpay, and winning will be a curse. Developing an algorithm for bidding that takes into account this curse requires the use of game theory.

Game theory could also be used by a bidder to understand the incentives of rival bidders and formulate strategies capable of altering their behaviour. In particular, if one could credibly commit to winning a licence, one could win the licence at zero cost, as the incentives for the rivals to bid when they know they are not going to win the licence, are likely to be low. An actual example of this could be the allocation in the April 1997 sale of wireless data frequencies, of the licences for several cities like Minneapolis, for $1.

To sum up, by identifying the individual incentives of each player in each auction design, game theory helped the designers and consultants in understanding the impact of the rules of the game on the behaviour of the actors. As McAfee and McMillan put it in their account: 'The role of theory is to show how people behave in various circumstances, and to identify the trade-offs involved in altering those circumstances.'

Questions

1 Briefly summarise the benefits to bidders of being familiar with game theory.

2 Does it help the sellers (here the government) to be aware of the principles underlying game theory?