week 11 1 COS 444 Internet Auctions: Theory and Practice Spring 2008 Ken Steiglitz

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.

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

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)

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 That is, how to compensate for the tendency to forget how likely it is for winning to be bad news

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 , after Julia Grant]

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.”

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

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”)

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

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

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