Continuous Implementation

Authors

  • Marion Oury,

    1. Théorie Économique, Modélisation, Application, Université de Cergy-Pontoise, Cergy-Pontoise, France; marionoury@gmail.com
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  • Olivier Tercieux

    1. Paris School of Economics, 48 boulevard Jourdan, 75 014 Paris, France; tercieux@pse.ens.fr
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    • We thank the editor and four anonymous referees for detailed comments that led to numerous improvements in the paper. We are also thankful to D. Bergemann, P. Jehiel, A. Kajii, T. Kunimoto, E. Maskin, N. Vieille, and seminar participants at Paris School of Economics, the EEA meeting in Budapest, Princeton University, the Institute for Advanced Study in Princeton, Rutgers University, McGill University, the World Congress of Game Theory at Northwestern, the Workshop on New Topics in Mechanism Design in Madrid, GRIPS Workshop on Global Games in Tokyo, the PSE-Northwestern joint workshop, and the Recent Developments in Mechanism Design conference held in Princeton. We are especially grateful to S. Morris for helpful remarks and discussions at various stages of this research. Joint authorship of O. Tercieux with D. Bergemann and S. Morris has greatly improved this version; in particular, the notion of interim rationalizable monotonicity was developed in discussions between D. Bergemann, S. Morris, and O. Tercieux. Finally, O. Tercieux thanks the Institute for Advanced Study at Princeton for financial support through the Deutsche Bank membership. He is also grateful to the Institute for its hospitality.


Abstract

In this paper, we introduce a notion of continuous implementation and characterize when a social choice function is continuously implementable. More specifically, we say that a social choice function is continuously (partially) implementable if it is (partially) implementable for types in the model under study and it continues to be (partially) implementable for types “close” to this initial model. Our results show that this notion is tightly connected to full implementation in rationalizable strategies.

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