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Constrained implementation

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  • Hayashi, Takashi
  • Lombardi, Michele

Abstract

Consider a society with two sectors (issues or objects) that faces a design problem. Suppose that the sector-2 dimension of the design problem is fixed and represented by a mechanism Γ2, and that the designer operates under this constraint for institutional reasons. A sector-1 mechanism Γ1 constrained implements a social choice rule φ in Nash equilibrium if for each profile of agents' preferences, the set of (pure) Nash equilibrium outcomes of the mechanism Γ1×Γ2 played by agents with those preferences always coincides with the recommendations made by φ for that profile. If this mechanism design exercise could be accomplished, φ would be constrained implementable. We show that constrained monotonicity, a strengthening of (Maskin) monotonicity, is a necessary condition for constrained implementation. When there are more than two agents, and when the designer can use the private information elicited from agents via Γ2 to make a socially optimal decision for sector 1, constrained monotonicity, combined with an auxiliary condition, is sufficient. This sufficiency result does not rule out any kind of complementarity between the two sectors.

Suggested Citation

  • Hayashi, Takashi & Lombardi, Michele, 2019. "Constrained implementation," Journal of Economic Theory, Elsevier, vol. 183(C), pages 546-567.
    • Handle: RePEc:eee:jetheo:v:183:y:2019:i:c:p:546-567
    DOI: 10.1016/j.jet.2019.06.007
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    References listed on IDEAS

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    Cited by:

    1. Malachy James Gavan & Antonio Penta, 2022. "Safe Implementation," Working Papers 1363, Barcelona School of Economics.
    2. Gavan, Malachy James & Penta, Antonio, 2022. "Safe Implementation," TSE Working Papers 22-1369, Toulouse School of Economics (TSE).

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    More about this item

    Keywords

    Constrained implementation; Mechanism design; Nash implementation;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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