The Complexity of Optimal Mechanism Design
Name
Daskalakis_The complexity.pdf
Size
256.37 KB
Format
Adobe PDF
Checksum (MD5)
9e7e82eae6d4a1df8378c50e6eddd991
Author(s)
Deckelbaum, Alan
Tzamos, Christos
Daskalakis, Konstantinos
Date Issued
2014
Journal
Proceedings of the Twenty-fifth Annual ACM-SIAM Symposium on Discrete Algorithms
Publisher
Society for Industrial and Applied Mathematics
Citation
Daskalakis, Constantinos, Alan Deckelbaum, and Christos Tzamos. “The Complexity of Optimal Mechanism Design.” Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms (December 18, 2013): 1302–1318.
Version
Original manuscript
Abstract
Myerson's seminal work provides a computationally efficient revenue-optimal auction for selling one item to multiple bidders [18]. Generalizing this work to selling multiple items at once has been a central question in economics and algorithmic game theory, but its complexity has remained poorly understood. We answer this question by showing that a revenue-optimal auction in multi-item settings cannot be found and implemented computationally efficiently, unless zpp ⊇ P[superscript #P]. This is true even for a single additive bidder whose values for the items are independently distributed on two rational numbers with rational probabilities. Our result is very general: we show that it is hard to compute any encoding of an optimal auction of any format (direct or indirect, truthful or non-truthful) that can be implemented in expected polynomial time. In particular, under well-believed complexity-theoretic assumptions, revenue-optimization in very simple multi-item settings can only be tractably approximated.
We note that our hardness result applies to randomized mechanisms in a very simple setting, and is not an artifact of introducing combinatorial structure to the problem by allowing correlation among item values, introducing combinatorial valuations, or requiring the mechanism to be deterministic (whose structure is readily combinatorial). Our proof is enabled by a flow-interpretation of the solutions of an exponential-size linear program for revenue maximization with an additional supermodularity constraint.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/1.9781611973402.96
