1. week 11 1 COS 444 Internet Auctions: Theory and Practice Spring 2008 Ken Steiglitz ken@cs.princeton.edu

2. week 112 Winner’s Curse o The paradigmatic experiment: bid on a jar of nickels o The systematic error is to fail to take into account the fact that winning may be an informative event! winning may be an informative event! o Caused by a cognitive illusion See Richard Thaler’s The Winner’s Curse: Paradoxes and Anomalies of Economic Life, Princeton University Press, 1992.

4. week 114 Winning is bad news, unless you shade o Suppose bidders are uncertain about their values V i, receiving noisy signals X i o Based on this information, your best estimate is E[V | X 1 ] o Suppose you, bidder 1, win the auction! o Then your new best estimate of your value is E[V | X 1, Y 1 < X 1 ] < E[V | X 1 ] --- where Y 1 is the highest of the other signals

5. week 115 Example: first-price auctions Common-value model: say the item has the same but unknown value to all bidders, and each bidder receives a noisy signal related to the true value Suppose the number of bidders increases. Then  According to the private-value equilibrium, you should increase your bid  Taking into account the Winner’s Curse, you should decrease your bid (often dominates)

6. week 116 Winner’s curse, con’t Important paper, which describes how to find a symmetric equilibrium: R.B. Wilson, “Competitive Bidding with Disparate Information,” Management Science 15, 7, March 1969, pp. 446-448. That is, how to compensate for the tendency to forget how likely it is for winning to be bad news

7. week 117 Empirical results o In the laboratory the Winner’s Curse is real and persistent o Observed in practice: oil industry, baseball free agents, book publishing o Even professional bidders from the commercial construction industry succumb; (Dyer at al. suggest they learn situation- specific rules rather than the right theory [Thaler, p. 56] ) o What do you do if you find your competitors are making consistent errors? Publish! [Thaler, pp. 61-62, after Julia Grant]

8. week 118 Capen et al.’s fortune cookie: “He who bids on a parcel what he thinks it is worth, will, in the long run, be taken for a cleaning.”

9. week 119 Interdependent Values In general, we relax two IPV assumptions: 1) Bidders are no longer sure of their values (as in the common-value case discussed in connection with the Winner’s Curse) 2) Bidders’ signals are statistically correlated; technically positively affiliated (see Milgrom & Weber 82, Krishna 02) Intuitively: if some subset of signals is large, it’s more likely that the remaining signals are large

10. week 1110 Major results in Milgrom & Weber For the general symmetric, affiliated- values model: o English > 2 nd -Price > 1 st -Price = Dutch -- (“revenue ranking”) o If the seller has private information, full disclosure maximizes price -- (“Honesty is the best policy”)

11. week 1111 Milgrom & Weber: Caveats o Symmetry assumption is crucial; results fail without it o English is Japanese button model o For disclosure result: seller must be credible, pre-committed to known policy o Game-theoretic setting assumes distributions of signals are common knowledge

12. week 1112 The linkage principle (after Krishna 02) Consider the price paid by the winner when her signal is x but she bids as if her value is z, denoted by W ( z, x ) Define the linkage : Sensitivity of expected price paid by winner to variations in her received signal when bid is held fixed

13. week 1113 The linkage principle, con’t Proposition: Two auctions with symmetric and increasing equilibria, and with W(0,0) = 0, are revenue-ranked by their linkages. Consequences: 1 st -Price: linkage L 1 = 0 2 nd -Price: price paid is linked through x 2 to x 1 ; so L 2 > 0 x 2 to x 1 ; so L 2 > 0 English: … through all signals to x 1 ; so L E > L 2 > L 1 L E > L 2 > L 1