Abstract

http://ssrn.com/abstract=1799085
 
 

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Mean Field Equilibria of Dynamic Auctions with Learning


Krishnamurthy Iyer


Stanford University - Management Science & Engineering

Ramesh Johari


Stanford University - Management Science & Engineering

Mukund Sundararajan


Google, Inc.

February 26, 2012


Abstract:     
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 which 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 known as 'mean field equilibrium' (MFE). The methodology assumes that agents optimize only with respect to long run average estimates of the distribution of other players' bids. We show a remarkable fact: in a mean field equilibrium, the agent has an optimal strategy where she bids truthfully according to a 'conjoint valuation'. The 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. Under mild conditions on the model, we show that an MFE exists, and that it is a good approximation to a 'rational' agent's behavior as the number of agents increases. Formally, if every agent 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 auction format and design on the auctioneer's revenue. In particular, we establish a dynamic version of the revenue equivalence theorem, and discuss optimal selection of reserve prices in dynamic auctions.

Number of Pages in PDF File: 49

Keywords: mean field equilibrium, dynamic auction markets, conjoint valuation

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Date posted: March 31, 2011 ; Last revised: February 27, 2012

Suggested Citation

Iyer, Krishnamurthy and Johari, Ramesh and Sundararajan, Mukund, Mean Field Equilibria of Dynamic Auctions with Learning (February 26, 2012). Available at SSRN: http://ssrn.com/abstract=1799085 or http://dx.doi.org/10.2139/ssrn.1799085

Contact Information

Krishnamurthy Iyer (Contact Author)
Stanford University - Management Science & Engineering ( email )
473 Via Ortega
Stanford, CA 94305-9025
United States
Ramesh Johari
Stanford University - Management Science & Engineering ( email )
473 Via Ortega
Stanford, CA 94305-9025
United States
Mukund Sundararajan
Google, Inc. ( email )
1600 Amphitheatre Parkway
Second Floor
Mountain View, CA 94043
United States
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