Border's theorem gives an intuitive linear characterization of the feasible interim allocation rules of a Bayesian single-item environment, and it has several applications in economic and algorithmic mechanism design. All known generalizations of Border's theorem either restrict attention to relatively simple settings or resort to approximation. This article identifies a complexity-theoretic barrier that indicates, assuming standard complexity class separations, that Border's theorem cannot be extended significantly beyond the state of the art.We also identify a surprisingly tight connection between Myerson's optimal auction theory, when applied to public project settings, and some fundamental results in the analysis of Boolean functions.
Bibliographical noteFunding Information:
Noam Nisan was partially supported by Israeli Academy of Sciencesnder Grant numbers 230/10 ISF and 1435/14 ISF administered by the Israeli Academy of Sciences. Tim Roughgarden was aupported in part by National Science Foundation NSF under Grant numbers CCF-1215965 NSF and CCF-1524062 NSF. Authors’ addresses: P. Gopalan, VMware, Inc., Palo Alto, CA; N. Nisan, Room A432, Rothberg building, School of Computer Science and Engineering, Hebrew University of Jerusalem; T. Roughgarden, Stanford University, 474 Gates Building, 353 Serra Mall, Stanford, CA 94305. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from email@example.com. © 2018 Association for Computing Machinery. 2167-8375/2018/11-ART18 $15.00 https://doi.org/10.1145/3274645
Noam Nisan was partially supported by Israeli Academy of Sciencesnder Grant numbers 230/10 ISF and 1435/14 ISF administered by the Israeli Academy of Sciences. Tim Roughgarden was aupported in part by National Science Foundation NSF under Grant numbers CCF-1215965 NSF and CCF-1524062 NSF.
© 2018 Association for Computing Machinery.
- Border's theorem
- Correlated values
- Myerson theory
- Optimal auctions