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Implementation Theory

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  • Eric Maskin
  • Tomas Sjostrom

    (School of Social Science, Institute for Advanced Study
    Department of Economics, Rutgers, the State University of New Jersey)

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science.
    • Handle: RePEc:ads:wpaper:0006
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    More about this item

    Keywords

    Implementation; Social Decision Making; Nash Equilibrium; Bayesian Implementation;
    All these keywords.

    JEL classification:

    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • B30 - Schools of Economic Thought and Methodology - - History of Economic Thought: Individuals - - - General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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