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.