Approximately Optimal Auction when Bidders have Private Budgets

ABSTRACT We tackle the problem of designing revenue maximizing auctions in the Bayesian framework, when bidders not only have private valuations but also private budgets. We consider the setting of selling divisible goods to multiple agents each with linear utilities, but agents cannot pay beyond their budget. We focus on the case when the auctioneer can check that bidders do not over-report their budgets, but bidders may under-report. We characterize all incentive-compatible auctions in this framework. Using this result and LP-rounding, we design 4 practically implementable auction mechanisms: proportional-sharing, conservative-sharing, fixed-queuing, and random queuing. The sharing auctions are similar to having a separate allocation table for each bidder, and scaling down appropriately to ensure that the total allocation does not exceed supply. The queuing auctions sort bidders according to some arbitrary priority, and allocate to bidders with higher priorities first. We show that the auctions achieve revenue approximation ratios of 4.08, 3.26, 5.83 and 3.73 respectively.