week 31 COS 444 Internet Auctions: Theory and Practice Spring 2010 Ken Steiglitz

week 32 Theory Order statistics pdf of k-th highest cdf of k-th highest Application to revenue calculation

week 33 pdf of k-th largest n choices for which drawn n f(x) dx ways

week 34

5 German tank problem Suppose tank numbers are sequential real numbers uniform on [0,N]. We capture k tanks. The expected max of k samples is So a reasonable estimate is (when values are integers, subtract 1)

week 36 Theory Order statistics pdf of k-th highest cdf of k-th highest Simple equilibrium calculation

week 37 First price, n bidders Suppose everyone else bids θv i Differentiate wrt b, set to 0  b = (1-1/n)v 1 (checks ) so θ = (1-1/n) works as equilibrium Quick and dirty equilibrium calculation for FP with iid uniform values

week 38 Theory Order statistics pdf of k-th highest cdf of k-th highest Simple equilibrium calculation Revenue equivalence w. uniform v’s

week 39 Revenue equivalence of FP & SP, uniform SP: E[price paid] = E[Y 2 ] = (n-1)/(n+1) E[value of winner] = E[Y 1 ] = n/(n+1) E[surplus of winner] = difference = 1/(n+1) FP: Equil. Bid is v*(n-1)/n E[surplus of winner] = E[v max /n] = 1/(n+1)

week 310 New directions: Sociology M. Shohat and J. Musch “Online auctions as a research tool: A field experiment on ethnic discrimination” Swiss Journal of Psychology 62 (2), 2003,

week 311 Shohat & Musch ’03 typical field experiment methodology Parallel items sold (30 DVDs), once with each experimental variable (mehmet.orgum vs. michael.ottersbach); and all other variables controlled as equal or randomized. Eg., Mehmet auctioned one randomly chosen half (A) the first week, and the other half (B) the second week; Michael auctioned B the first week and A the second.

week 312 Shohat & Musch ’03 typical field experiment methodology Other variables controlled as carefully as possible (for example, DVDs not shipped first week, so no feedback appeared for either “seller”) Statistical tests of results (usually probability of observing results assuming null hypothesis > 95%)

week 313 Shohat & Musch ’03 typical field experiment methodology Discussion, interpretation Alternative explanations (not high enough financial risk; not social setting; “Mehmet” not recognized as Turk; presentation might have seemed “German” (!); buyers may turn to Turkish sellers only after not finding it from a German seller, etc.) Other work

week 314 Shohat & Musch ’03 typical field experiment methodology Privacy, ethics: Buyers not informed, no consent! Data hidden after experiment (“make profile private”, anonymity guaranteed) Experiments kept within rules (no surveys, eg) Deals kept scrupulously honest

week 315 Field experiments: Testing theory LR 99: tests FP-Dutch and SP-English revenue equivalence online (pre-eBay) Katkar-LR 00: tests public vs. secret reserve on eBay LR 00: tests effects of reserves in FP online (pre-eBay)

week 316 Lucking-Reiley 99Lucking-Reiley 99: Magic on the internet (his PhD dissertation) Pre-eBay Tests revenue equivalence: FP=Dutch and SP=English

week 317 LR 99 (con’t) Newsgroup: rec.games.deckmaster, now an impossible experiment. 1995: 6000 messages/week, highest volume on the internet. 90% Magic cards. Variety of auctions observed, all but Vickrey Sold matched pairs, first with FP first, then Dutch; then with Dutch first, then FP. Similarly for English-SP. Experiments were profitable…$1600 purchase sold for $2000.

week 318 LR 99 (con’t) Results: Dutch > FP Revenue in Dutch > FP by 30% (opposite to lab experiments) Explain! (while strategically equilvalent) English ≈ SP Revenue in English ≈ SP (while weakly strategically equivalent) Revenue equivalence between pairs left open