Chapter 5 Implementation theory

Eric Maskin, Tomas Sjöström

Research output: Chapter in Book/Report/Conference proceedingChapter

108 Scopus citations

Abstract

The implementation problem is the problem of designing a mechanism (game form) such that the equilibrium outcomes satisfy a criterion of social optimality embodied in a social choice rule. If a mechanism has the property that, in each possible state of the world, the set of equilibrium outcomes equals the set of optimal outcomes identified by the social choice rule, then the social choice rule is said to be implemented by this mechanism. Whether or not a social choice rule is implementable may depend on which game-theoretic solution concept is used. The most demanding requirement is that each agent should always have a dominant strategy, but mainly negative results are obtained in this case. More positive results are obtained using less demanding solution concepts such as Nash equilibrium. Any Nash-implementable social choice rule must satisfy a condition of "monotonicity". Conversely, any social choice rule which satisfies monotonicity and "no veto power" can be Nash-implemented. Even non-monotonic social choice rules can be implemented using Nash equilibrium refinements. The implementation problem can be made more challenging by imposing additional requirements on the mechanisms, such as robustness to renegotiation and collusion. If the agents are incompletely informed about the state of the world, then the concept of Nash equilibrium is replaced by Bayesian Nash equilibrium. Incentive compatibility is a necessary condition for Bayesian Nash implementation, but in other respects the results closely mimic those that obtain with complete information.

Original languageEnglish (US)
Title of host publicationHandbook of Social Choice and Welfare
EditorsKenneth Arrow, Kotaro Suzumura, Amartya Sen
Pages237-288
Number of pages52
DOIs
StatePublished - 2002
Externally publishedYes

Publication series

NameHandbook of Social Choice and Welfare
Volume1
ISSN (Print)1574-0110

All Science Journal Classification (ASJC) codes

  • Sociology and Political Science
  • Economics and Econometrics

Keywords

  • implementation
  • mechanism design
  • social choice

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