Revenue Maximization and Ex-Post Budget Constraints
Name
1605.02054.pdf
Description
Submitted version
Size
250.5 KB
Format
Adobe PDF
Checksum (MD5)
757be5cc73a1713a318b3d5f50a01d3f
Author(s)
Daskalakis, Konstantinos
Devanur, Nikhil R.
Weinberg, S. Matthew
Date Issued
November 2018
Journal
ACM Transactions on Economics and Computation
Publisher
Association for Computing Machinery (ACM)
Citation
Daskalakis, Constantinos et al. "Revenue Maximization and Ex-Post Budget Constraints." ACM Transactions on Economics and Computation 6, 3-4 (November 2018): 20.
Version
Original manuscript
Abstract
We consider the problem of a revenue-maximizing seller with m items for sale to n additive bidders with hard budget constraints, assuming that the seller has some prior distribution over bidder values and budgets. The prior may be correlated across items and budgets of the same bidder, but is assumed independent across bidders. We target mechanisms that are Bayesian incentive compatible, but that are ex-post individually rational and ex-post budget respecting. Virtually no such mechanisms are known that satisfy all these conditions and guarantee any revenue approximation, even with just a single item. We provide a computationally efficient mechanism that is a 3-approximation with respect to all BIC, ex-post IR, and ex-post budget respecting mechanisms. Note that the problem is NP-hard to approximate better than a factor of 16/15, even in the case where the prior is a point mass. We further characterize the optimal mechanism in this setting, showing that it can be interpreted as a distribution over virtual welfare maximizers.
We prove our results by making use of a black-box reduction from mechanism to algorithm design developed by Cai et al. Our main technical contribution is a computationally efficient 3-approximation algorithm for the algorithmic problem that results from an application of their framework to this problem. The algorithmic problem has a mixed-sign objective and is NP-hard to optimize exactly, so it is surprising that a computationally efficient approximation is possible at all. In the case of a single item (m=1), the algorithmic problem can be solved exactly via exhaustive search, leading to a computationally efficient exact algorithm and a stronger characterization of the optimal mechanism as a distribution over virtual value maximizers.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1145/3274647
