Comments on Milgrom (1989) and McMillan (1994) on “Auctions” Nick Parker Econ 594ER October 29, 2007

Milgrom I The ‘Winner’s Curse’ –Painter wins a bid for an unfamiliar job but costs run much higher than anticipated. Why? –Because each individual bidder’s estimates of costs are unbiased, the lowest bid must be biased downward –Remedy: spend time researching costs and bid conservatively Equivalence of auction institutions –First-price auctions sealed bid Dutch –Second-price Q: What is the dominant strategy is a 2 nd price auction (equivalent to English outcry)? –Case 1: b 1 > v 1, v 2 = b 2 b 1 > b 2 and b 2 > v 1 implies net loss b 1 > b 2 and b 2 < v 1 implies gain of v 1 - v 2 –Case 2: b 1 = v 1,, v 2 = b 2 b 1 > b 2 implies gain of v 1 - v 2 Q: Equivalent dominant strategy under standard assumptions? Yes, in theory but doesn’t happen in small-stakes lab experiments –And it can be shown for all cases not given here that b1 = v1 dominates

Milgrom II Why can we get sub-optimal allocation with first-price auctions? –Bill has $101 value on good, and knows Fred values good with 0.8 probability at $50 and 0.2 probability at $75 –Bill will max P(winning)∙E(payout|winning) and it is never optimal to bid more than $62. Comparison among auctions –There are theoretically efficient auctions for a myriad of institutional settings. However, auctions in the real-world are simple –In fixed-quantity environments, English outcry is most efficient. However, these require presence of bidders and 2 nd -price sealed auctions can be corrupted. Q: What is the main point of the paper? Can we rely on auctions to achieve efficient allocation of resources?

McMillan I How would the U.S. government assign spectrum rights no longer reserved by military? –Administrative assignment, lottery, auction, first-possession –Q: Why not assign by lottery or first-possession and allow trade? Selling spectrum rights via auction. –Thousands of 10-year spectrum licenses to be sold circa 1994 to cell phone companies, cable TV companies etc. –Bidders face risks, but could make huge profits –FCC cares about revenue but also wants ownership by minorities and wants to limit negative publicity How did game theorists inform the auction design?

McMillan II Lessons learned from other spectrum-rights auctions –New Zealand 2 nd -price debacle 1 firm bids NZ$100,000 and pays 2 nd -bid of NZ$6 Cellular licenses fetched NZ$36 million v. NZ$240 million estimate Lessons: no reserve prices required, govt publicized 1 st price –Australia 1 st -price auction UCom and Hi Vision won with high bids but neglected to pay Lesson 1: there was no penalty for default to discipline bids so that bids conveyed no real information. Lesson 2: Fine print matters – oversight in auction design will be exploited

McMillan III: Questions and solutions in U.S. auction design Sealed-bid v. open auction –OA gives bidders more info, which reduces winner’s curse, and increases the bids of the risk averse but bidder collusion is easier in OA –Middle ground solution: use multiple rounds of sealed bids, announce leading bids but not bidder identity Simultaneous v. sequential auction of all licenses –sequential is easier to understand and administer, but impedes aggregation of licenses –Solution was to allow simultaneous bidding over multiple licenses but create stopping points to prevent perpetual bidding –Withdrawal penalties were imposed How should licenses be assigned to designated bidders –Use special auctions? –Subsidize the bids of designated bidders? Q: Was economic theory needed or would untrained smart people give similar advice? Did lab experiments identify pitfalls? Why not use lotteries with ex post trade?