2018년 3월 15일 목요일

탐색:// 비크리(Vickrey) 경매의 약점


※ 발췌 (excerpt):


출처 1: The Lovely but Lonely Vickrey Auction (Lawrence M. Ausubel and Paul Milgrom, 2006)

4. Weaknesses of the VCG Mechanism

Despite the attractiveness of the dominant-strategy property, the VCG mechanism also has several possible weaknesses:

- low (or zero) revenues;
- non-monotonicity of the seller's revenues in the set of bidders and the amounts bid;
- vulnerability to collusion by a coalition of losing bidders; and
- vulnerability to the use of multiple bidding identities by a single bidder.

It will be seen later in this chapter that a simple and intuitive condition on individual bidders characterizes whether these deficiencies are present. In economic environments where every bidder has ^substitutes preferences^, the above-listed weaknesses will never occur. However, if there is but a single bidder whose preferences violate the substitutes condition, then with an appropriate choice of values for remaining biddes (even if the latter values are restricted to be additive),  all of the above-listed weaknesses will be present.

In what follows, we will limit attention to auctions of multiple items, in which different bidders may want different numbers of different packages of items. One obvious reason for the disuse of the VCG mechanism for large-scale applications with diverse items is the same as for other "combinatorial" or "package" auctions: complexity in all aspects of its implementation. ( ... ... )

Complexity, however, cannot be the whole explanation of the rarity of the VCG mechanism. Combinatorial auctions of other kinds have been adopted for a variety of procurement applications, from school milk programs in Chile to bus route services in London, England. Small-scale combinatorial auctions are technically feasile, so we are forced to conclude that VCG rules have not been employed even when they are feasible.

Analyses of the VCG mechanism often exclude any discussion of the auction revenues. This is an important omission. For private sellers, revenues are the primary concern. Even in the government-run spectrum auctions, in which priorities like allocational efficiency, promoting ownership by small businesses or women- or minority-owned businesses, rewarding innovation, and avoiding concentration of ownership are weighty considerations, one of the performance measures most emphasized by the public and politcians alike is the final auction revenue.[주]3

Against this background, it is particularly troubling that the Vickrey auction revenues can be very low or zero, even when the items being sold are quite valuable and competition is ample. For example,[주]4

consider a hypotentical auction of two spectrum licences to three bidders. Suppose that bidder 1 wants only the package of two licences and is willing to pay $2 billion, while the bidders 2 and 3 are both willing to pay $2 billion for a single license. The VCG mechanism assigns the licenses efficiently to bidders 2 and 3. The price paid by bidder 2 is the difference in the value of one license or two licenses to the remaining bidders. Since the difference is zero, the price is zero! The same conclusion applies symmetrically to bidder 3, so the total auction revenues are zero.

Notice that, in this example, if the government had sold the two licenses as an indivisible whole, then it would have had three bidders each willing to pay $2 billion  for the combined licenses. That is ample competition: an ascending auction would have been expected to lead to a price of $2 billion. This revenue deficiency of the VCG mechanism is decisive to reject it for most practical applications.

Closely related to the revenue deficiency of the Vickrey auction is the non-monotonicity of seller revenues both in the set of bidders and in the amounts bid. In the preceding example, if the third bidder were absent of if its value for a license were reduced from $2 billion to zero, then the seller's revenues in the VCG auction would increase from $0 to $2 billion. This non-monotonicity is not only a potential public relations problem but also creates loopholes and vulnerabilities that bidders can sometimes exploit.

One is the Vickrey design's vulnerability to collusion, even by losing bidders. This can be illustrated by a variant of the preceding example, in which bidde 1's vales are unchanged but bidders 2 and 3 have their values reduced so that each is willing to pay only $0.5 billion to acquire a single license. The change in values alters the efficient allocation, making bidders 2 and 3 losers in the auction. However, notice that if the bidders each bid $2 billion for their individual licenses, then the outocme will be the same above: each will win one license at a price of zero! ( ... ... )


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