Internet and Network Economics
Volume 4858 of the series Lecture Notes in Computer Science pp 269-280
Stochastic Mechanism Design
- Samuel IeongAffiliated withDepartment of Computer Science, Stanford University
- , Anthony Man-Cho SoAffiliated withDepartment of Sys. Eng. & Eng. Mgmt., The Chinese University of Hong Kong
- , Mukund SundararajanAffiliated withDepartment of Computer Science, Stanford University
Abstract
We study the problem of welfare maximization in a novel setting motivated by the standard stochastic two-stage optimization with recourse model. We identify and address algorithmic and game-theoretic challenges that arise from this framework. In contrast, prior work in algorithmic mechanism design has focused almost exclusively on optimization problems without uncertainty. We make two kinds of contributions.
First, we introduce a family of mechanisms that induce truth-telling in general two-stage stochastic settings. These mechanisms are not simple extensions of VCG mechanisms, as the latter do not readily address incentive issues in multi-stage settings. Our mechanisms implement the welfare maximizer in sequential ex post equilibrium for risk-neutral agents. We provide formal evidence that this is the strongest implementation one can expect.
Next, we investigate algorithmic issues by studying a novel combinatorial optimization problem called the Coverage Cost problem, which includes the well-studied Fixed-Tree Multicast problem as a special case. We note that even simple instances of the stochastic variant of this problem are #P-Hard. We propose an algorithm that approximates optimal welfare with high probability, using a combination of sampling and supermodular set function maximization—the techniques may be of independent interest. To the best of our knowledge, our work is the first to address both game-theoretic and algorithmic challenges of mechanism design in multi-stage settings with data uncertainty.
- Title
- Stochastic Mechanism Design
- Book Title
- Internet and Network Economics
- Book Subtitle
- Third International Workshop, WINE 2007, San Diego, CA, USA, December 12-14, 2007. Proceedings
- Pages
- pp 269-280
- Copyright
- 2007
- DOI
- 10.1007/978-3-540-77105-0_26
- Print ISBN
- 978-3-540-77104-3
- Online ISBN
- 978-3-540-77105-0
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- 4858
- Series ISSN
- 0302-9743
- Publisher
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
- Topics
- Industry Sectors
- eBook Packages
- Editors
- Authors
-
- Samuel Ieong (1)
- Anthony Man-Cho So (2)
- Mukund Sundararajan (1)
- Author Affiliations
-
- 1. Department of Computer Science, Stanford University,
- 2. Department of Sys. Eng. & Eng. Mgmt., The Chinese University of Hong Kong,
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