Speaker: Aaron Roth, University of Pennsylvania

Title: Do Prices Coordinate Markets?

Abstract:

Market equilibrium prices have a remarkable property: they allow each buyer to purchase a bundle of goods that she finds the most desirable,while guaranteeing that the induced allocation over all buyers is feasible, and globally maximizes social welfare. However, this clean story has two important caveats:

1) First, the prices may induce indifferences.  In general, buyers may need to coordinate with one another to resolve these indifferences, so the prices alone are not sufficient to coordinate the market.

2) Second, although we know natural procedures which converge toequilibrium prices on a fixed population, in practice buyers observe prices without participating in an auction. If prices represent distributional information, how much data is needed to "learn" good prices?

To better understand the performance of equilibrium prices when facing these two problems, we give results of two sorts. First, we show a mild condition under which the equilibrium prices induce low over-demand for arbitrary tie-breaking by buyers. Second, we use techniques from learning theory to argue that the over-demand and welfare induced by a price vector on an unknown distribution of buyers is small, even when computed from a sample of buyers representing a relatively small market.

Combining these two results implies that under a mild condition, the equilibrium prices computed in a market are guaranteed to induce both low over-demand and high welfare when used in a new market, in which agents are sampled independently from the same distribution, when ever the number of agents is larger than the number of commodities in the market.

Joint work with: Justin Hsu, Jamie Morgenstern, Ryan Rogers, and Rakesh Vohra.

Biography:

Aaron Roth is the Raj and Neera Singh assistant professor of Computer and Information Sciences at the University of Pennsylvania, affiliated with the Warren Center for Network and Data Science. Previously, he received his PhD from Carnegie Mellon University and spent a year as a postdoctoral researcher at Microsoft Research New England. He is the recipient of an Alfred P. Sloan Research Fellowship, an NSF CAREER award, and a Yahoo! ACE award.  His research focuses on the algorithmic foundations of data privacy, game theory and mechanism design, and the intersection of the two topics.Together with Cynthia Dwork, he is the author of the book “The Algorithmic Foundations of Differential Privacy.”