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SUMMARY:Mean Field Equilibria of Dynamic Auctions with Learning - Krishnam
 urthy Iyer\, Stanford University
DTSTART:20120320T090000Z
DTEND:20120320T100000Z
UID:TALK36939@talks.cam.ac.uk
CONTACT:Microsoft Research Cambridge Talks Admins
DESCRIPTION:We study learning in a dynamic setting where identical copies 
 of a good are sold over time through a sequence of second price auctions. 
 Each agent in the market has an *unknown* independent private valuation wh
 ich determines the distribution of the reward she obtains from the good\; 
 for example\, in sponsored search settings\, advertisers may initially be 
 unsure of the value of a click. Though the induced dynamic game is complex
 \, we simplify analysis of the market using an approximation methodology k
 nown as *mean field equilibrium* (MFE). The methodology assumes that agent
 s optimize only with respect to long run average estimates of the distribu
 tion of other players' bids.  We show a remarkable fact: in a mean field e
 quilibrium\, the agent has an optimal strategy where she bids truthfully a
 ccording to a *conjoint valuation*. \nThe conjoint valuation is the sum of
  her current expected valuation\, together with an overbid amount that is 
 exactly the expected marginal benefit to one additional observation about 
 her true private valuation. \nUnder mild conditions on the model\, we show
  that an MFE exists\, and that it is a good approximation to a rational ag
 ent's behavior as the number of agents increases. Formally\, if every agen
 t except one follows the MFE strategy\, then the remaining agent's loss on
  playing the MFE strategy converges to zero as the number of agents in the
  market increases. We conclude by discussing the implications of the aucti
 on format and design on the auctioneer's revenue.  In particular\, we esta
 blish a dynamic version of the revenue equivalence theorem\, and discuss o
 ptimal selection of reserve prices in dynamic auctions.\n\n(Joint work wit
 h Ramesh Johari and Mukund Sundararajan)
LOCATION:Large lecture theatre\, Microsoft Research Ltd\, 7 J J Thomson Av
 enue (Off Madingley Road)\, Cambridge
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