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• Introduction to Decision Making Theory 
• Introduction to Mechanism Design 
• Theory of Repeated Games 

3G Auctions in UK: Q&A

The last chapter of Paul Klemperer's famous auction book provides non-technical answers to the FAQs on spectrum auctions, especially on the 3G auction that he (and Ken Binmore) designed and implemented in the UK.



The chapter titled "Were Auctions a Good Idea?" is based on his newspaper article, "The Wrong Culprit for Telecom Trouble" appeared in Financial Times (Nov. 26, 2002) where he listed three typical critics against 3G auctions:

The critics assume three things, that 

1: the telecoms companies paid more for the licenses than they thought the licenses were worth

2: this expenditure has reduced investment in 3G

3: it destroyed the telecoms companies' market value

Paul answers to each question as follows:

1. It is now hard to imagine any company voluntarily paid billions for a 3G license. But volunteer they all did - and they celebrated their victories. (...) Like any other market, an auction simply matches willing buyers and willing sellers - it cannot protect them against their own mistakes.

2. The auction fees are history; they have (almost) all been paid in full, cannot be recouped by cutting investment, and make no difference to its profitability. (...) Investment in 3G, as in anything else, is primarily motivated by attractive returns in the future - not by money spent in the past.

3. All in all, it seems a stretch to blame $100bn of shareholder misery on $100bn of 3G license fees.

Then, he concludes the article by saying:

There is nothing special about an auction: it is just another market. Buying houses or shares at the peak of a housing or stock-market boom does not entitle anyone to compensation. Why should we make an exception for the phone companies?

(...)

The main effect of the license fees was simply to transfer $100bn from shareholders around the world to certain European governments. This was both equitable, since the companies were buying a public asset that they valued this highly at the time, and efficient, since such a lump sum transfer is much more efficient than most forms of taxation. Efficient, equitable and voluntary government funding is not easy to find: perhaps we should be more enthusiastic about it.

Auction theory: Myerson and mechanism design approach

Continued from the previous two articles, we still focus on Introduction of the auction book:

After referring early literature on auction theory, the authors introduce mechanism design theory and explain Myerson's path-breaking contribution.

The early work of Vickrey, Wilson, and Milgrom was largely focused on an equilibrium analysis and comparison of standard auction formats. Myerson led the development of mechanism design theory, which enables the researcher to characterize equilibrium outcomes of all auction mechanisms, and identify optimal mechanisms - those mechanisms that maximize some objective, such as revenues. His first application was to auctions.

Myerson (1981) determined the revenue-maximizing auction with risk-neutral bidders and independent private information. He also proved a general revenue equivalence theorem that says that revenues depend fundamentally on how the items are assigned - any two auction formats that lead to the same assignment of the items yield the same revenues to the seller.

The trick in Myerson's analysis was recognizing that any auction can be represented as a direct mechanism in which bidders simultaneously report their private information and then the mechanism determines assignments and payments based on the vector of reports. For any equilibrium of any auction game, there is an equivalent direct mechanism in which bidders truthfully report types and agree to participate. Hence, without loss of generality we can look at incentive compatible and individually rational mechanisms to understand properties of all auction games. Incentive compatibility respects the fact that the bidders have private information about their values; individual rationality respects the bidders voluntary participation decision. This key idea is known as the revelation principle (Myerson, 1979).

The following is a brief summary of other related papers.

Myerson and Satterthwaite (1983)

• applied revelation principle
• proved the general impossibility of efficient bargaining

Related Papers

• Cramton, GIbbons, and Klemperer (1987) showed that efficiency becomes possible when the traders jointly own the items
• Wilson (1993) also showed efficient mechanisms when the roles of buyers and sellers are not fixed ex ante

References
Cramton, Gibbons, and Klemperer, "Dissolving a Partnership Efficiently," Econometrica, 1987.
Myerson, "Incentive Compatibility and the Bargaining Problem," Econometrica, 1979.
Myerson, "Optimal Auction Design," Mathmatics of Operations Research, 1981.
Myerson and Satterthwaite,  "Efficient Mechanism for Bilateral Trading," Journal of Economic Theory, 1983.
Wilson, "Design of Efficient Trading Procedures," in Friedman and Rust ed., The Double Auction Market: Institutions, Theories, and Evidence, Addison-Wesley Publishing Company, 1993.