Implementation with a bounded action space

Liad Blumrosen*, Michal Feldman

*Corresponding author for this work

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

16 Scopus citations

Abstract

While traditional mechanism design typically assumes isomorphism between the agents' type- and action spaces, in many situations the agents face strict restrictions on their action space due to, e.g., technical, behavioral or regulatory reasons. We devise a general framework for the study of mechanism design in single-parameter environments with restricted action spaces. Our contribution is threefold. First, we characterize sufficient conditions under which the information-theoretically optimal social-choice rule can be implemented in dominant strategies, and prove that any multilinear social-choice rule is dominant-strategy implementable with no additional cost. Second, we identify necessary conditions for the optimality of action-bounded mechanisms, and fully characterize the optimal mechanisms and strategies in games with two players and two alternatives. Finally, we prove that for any multilinear social-choice rule, the optimal mechanism with k actions incurs an expected loss of O(1/k2) compared to the optimal mechanisms with unrestricted action spaces. Our results apply to various economic and computational settings, and we demonstrate their applicability to signaling games, public-good models and routing in networks.

Original languageAmerican English
Title of host publicationProceedings of the 7th ACM Conference on Electronic Commerce 2006
PublisherAssociation for Computing Machinery (ACM)
Pages62-71
Number of pages10
ISBN (Print)1595932364, 9781595932365
DOIs
StatePublished - 2006
Event7th ACM Conference on Electronic Commerce - Ann Arbor, MI, United States
Duration: 11 Jun 200615 Jun 2006

Publication series

NameProceedings of the ACM Conference on Electronic Commerce
Volume2006

Conference

Conference7th ACM Conference on Electronic Commerce
Country/TerritoryUnited States
CityAnn Arbor, MI
Period11/06/0615/06/06

Keywords

  • Communication Complexity
  • Implementation
  • Mechansm Design
  • Single-Crossing Condition

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