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Stochastic Mechanism Design

(Extended Abstract)
  • Samuel Ieong
  • Anthony Man-Cho So
  • Mukund Sundararajan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4858)

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.

Keywords

Incentive Compatibility Welfare Maximization Sample Average Approximation Social Welfare Maximizer Coverage Cost 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Samuel Ieong
    • 1
  • Anthony Man-Cho So
    • 2
  • Mukund Sundararajan
    • 1
  1. 1.Department of Computer Science, Stanford University 
  2. 2.Department of Sys. Eng. & Eng. Mgmt., The Chinese University of Hong Kong 

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