Competitive auctions and digital goods
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Multi-unit auctions with budget-constrained bidders
Proceedings of the 6th ACM conference on Electronic commerce
Revenue maximization when bidders have budgets
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Multi-unit Auctions with Budget Limits
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Budget constrained auctions with heterogeneous items
Proceedings of the forty-second ACM symposium on Theory of computing
Polyhedral clinching auctions and the adwords polytope
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Auctions with heterogeneous items and budget limits
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Generalized Partition Mechanism: Framework for Combining Multiple Strategy-Proof Mechanisms
WI-IAT '12 Proceedings of the The 2012 IEEE/WIC/ACM International Joint Conferences on Web Intelligence and Intelligent Agent Technology - Volume 02
Optimal auctions via the multiplicative weight method
Proceedings of the fourteenth ACM conference on Electronic commerce
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In this paper, we consider the problem of designing incentive compatible auctions for multiple (homogeneous) units of a good, when bidders have private valuations and private budget constraints. When only the valuations are private and the budgets are public, Dobzinski et al [8] show that the adaptive clinching auction is the unique incentive-compatible auction achieving Pareto-optimality. They further show that this auction is not truthful with private budgets, so that there is no deterministic Pareto-optimal auction with private budgets. Our main contribution is to show the following Budget Monotonicity property of this auction: When there is only one infinitely divisible good, a bidder cannot improve her utility by reporting a budget smaller than the truth. This implies that the adaptive clinching auction is incentive compatible when over-reporting the budget is not possible (for instance, when funds must be shown upfront). We can also make reporting larger budgets suboptimal with a small randomized modification to the auction. In either case, this makes the modified auction Pareto-optimal with private budgets. We also show that the Budget Monotonicity property does not hold for auctioning indivisible units of the good, showing a sharp contrast between the divisible and indivisible cases. The Budget Monotonicity property also implies other improved results in this context. For revenue maximization, the same auction improves the best-known competitive ratio due to Abrams [1] by a factor of 4, and asymptotically approaches the performance of the optimal single-price auction. Finally, we consider the problem of revenue maximization (or social welfare) in a Bayesian setting. We allow the bidders have public size constraints (on the amount of good they are willing to buy) in addition to private budget constraints. We show a simple poly-time computable 5.83-approximation to the optimal Bayesian incentive compatible mechanism, that is implementable in dominant strategies. Our technique again crucially needs the ability to prevent bidders from over-reporting budgets via randomization. We show the approximation result via designing a rounding scheme for an LP relaxation of the problem, which may be of independent interest.