Auction theory: Vickrey and early literature

Continued from the previous post, let me quote interesting parts from the editors' introductory summary.The following nicely illustrates the contribution of the pioneer of auction theory, William Vickrey.

Vickrey's seminal paper (Vickrey, 1961), mentioned in his 1996 Nobel Prize in economics, introduced the independent private value model, demonstrated equilibrium bidding behavior in a first-price auction, and then showed that truthful bidding could be induced as a dominant strategy by modifying the pricing rule: let each bidder pay the social opportunity cost of his winnings, rather than his bid. Finally, he showed in an example what would later be proven generally as the revenue equivalence theorem: different auction mechanisms that result in the same allocation of goods yield the same revenue to the seller.

Then, the authors explain a few important papers in the early literature of auction theory since Vickrey. The followings are my summary.

Wilson (1969)

• (pure) common value
• first analysis of equilibrium bidding with common values
• demonstrated the importance to avoid (what would be later called) the winner's curse

Milgrom (1981)

• common + private values
• discovered the importance of monotone likelihood ratio property (MLRP)
• showed that MLRP + conditional independence implies that

1. bidders use monotonic bidding strategies
2. a monotonic strategy satisfying the first-order condition constitutes an equilibrium

Milgrom and Weber (1982)

• affiliated values: if one bidder has a high signal of value, it is more likely that the signals of the other bidders are high
• showed that under affiliated values

1. Vickrey's revenue equivalence result no longer holds when we introduce a common value element
2. ascending auctions yield higher revenues than sealed-bid auctions

References
Milgrom, "Rational Expectations, Information Acquisition, and Competitive Bidding," Econometrica, 1981.
Milgrom and Weber, "A Theory of Auctions and Competitive Bidding," Econometrica, 1982.
Vickrey, "Counterspeculation, Auctions, and Competitive Sealed Tenders," Journal of Finance, 1961.
Wilson, "Competitive Bidding with Disparate Information," Management Science, 1969.