Optimal Auctions with Budget Constraints


August 11, 2010


Rakesh Vohra


Kellogg School of Management, Northwestern


We consider an environment where potential buyers of an indivisible good have
liquidity constraints, in that they cannot pay more than their `budget’
regardless of their valuation. A buyer’s valuation for the good as well as her
budget are her private information. We derive constrained-efficient and revenue
maximizing auctions for this setting. In general, the optimal auction
requires ‘pooling’ both at the top and in the middle despite the maintained
assumption of a monotone hazard rate. Further, the auctioneer will never find
it desirable to offer lump sum subsidies to bidders with low budgets.

On a technical note, our analysis is based on the `reduced form’ representation of auctions, which enables one to exploit a polymatroid representation of auctions. This polymatroid representation is useful in other applications, time permitting, will be outlined.


Rakesh Vohra

Rakesh Vohra was educated at University College London, the LSE and the University of Maryland. He is currently the John L. & Helen Kellogg Professor of Managerial Economics at the Kellogg School of Management as well as Director of the Center for Mathematical Studies in Economics and Management Science. His research interests are in pricing, auction theory and game theory.