Comments on Milgrom (1989) and McMillan (1994) on “Auctions”

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

2. 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 2nd price auction (equivalent to English outcry)? • Case 1: b1 > v1, v2 = b2 • b1 > b2 and b2 > v1 implies net loss • b1 > b2 and b2 < v1 implies gain of v1 - v2 • Case 2: b1 = v1,, v2 = b2 • b1 > b2 implies gain of v1 - v2 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

3. Milgrom II • Why can we get sub-optimal allocation with first-price auctions? • Billhas $101 value on good, and knows Fredvalues good with 0.8 probability at $50 and 0.2 probability at $75 • Billwill 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 2nd-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?

4. 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?

5. McMillan II • Lessons learned from other spectrum-rights auctions • New Zealand 2nd-price debacle • 1 firm bids NZ$100,000 and pays 2nd-bid of NZ$6 • Cellular licenses fetched NZ$36 million v. NZ$240 million estimate • Lessons: no reserve prices required, govt publicized 1st price • Australia 1st-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

6. 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?