Robust synthesis in mechanism design

Georgios Kotsalis*, Jeff S. Shamma

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

5 Scopus citations

Abstract

This paper considers two topics in mechanism design: fragility of optimal auctions and computationally constructive procedures for dynamic mechanisms. The first part of the paper considers the well studied topic in mechanism design of optimal auctions, i.e., auctions that produce maximal revenue. The design of an optimal auction in a general setting requires the principal to have complete knowledge of the probabilistic beliefs of the agents (bidders). This work shows that such an assumption leads to fragile designs in which a slight perturbation to these beliefs can alter the outcome of the auction significantly. We propose an alternative approach where the designer takes into account a nominal environment and provides incentives that are robust to perturbations on the beliefs of the agents. Using the theory of robust optimization, we find relevant uncertainty classes for which the proposed robust mechanisms have the same computational complexity as the nominal designs. The second part of the paper discusses dynamic mechanism design. Whereas standard mechanism design presumes a one shot scenario, dynamic mechanism design considers perpetual phenomena, e.g., the allocation of a limited resource to transient users. The dynamic mechanism problem has received considerable attention given the wealth of applications. Most work has concentrated on finding appropriate conditions according to which static designs have natural extensions to the dynamic setting. This paper considers optimal dynamic mechanisms using tools from robust control theory. In this framework the design of incentives for a desired social planner's policy reduces to the search of a storage function, analogous to synthesis problems involving dissipation inequalities. For specific structures, optimizing the incentives reduces to solving a linear program.

Original languageEnglish (US)
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
Pages225-230
Number of pages6
DOIs
StatePublished - Dec 1 2010
Event2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States
Duration: Dec 15 2010Dec 17 2010

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other2010 49th IEEE Conference on Decision and Control, CDC 2010
CountryUnited States
CityAtlanta, GA
Period12/15/1012/17/10

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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