CAM Colloquium: Kris Iyer, School of Operations Research and Information Engineering Cornell University

Friday, September 27, 2013 at 3:30pm Frank H. T. Rhodes Hall, 655 CAM Colloquium: Kris Iyer (Cornell) - Mean Field Equilibria of Dynamic Auctions Many auction markets are characterized by repeated interactions among participants with dynamic preferences arising out of budget constraints, demand constraints or incomplete information about the auctioned good; for example, in sponsored search settings, advertisers may initially be unsure of the value of a click. The standard game theoretic concept to analyze such dynamic interactions, namely a perfect Bayesian equilibrium, is often too complex for analysis, and in addition the behavior suggested by the equilibrium strategies often do not match with actual behavior of auction participants. To overcome these hurdles, we consider an approximation methodology known as *mean field equilibrium* to simplify the analysis of dynamic auctions. The methodology, inspired by a large market approximation, assumes that agents optimize only with respect to the long run average estimates of the distribution of other players' bids. We use the methodology to study learning in a dynamic auction market 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. 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 on auction design. Based on joint work with Ramesh Johari (Stanford) and Mukund Sundararajan (Google).