Abstract
In this paper, we study implementation in “economic environments”. It is shown that there is a dense subset of the set of preference profiles such that given an arbitrary social choice function, f, and ε>0, there exists another social choice function, f ε, within ε of f uniformly and implementable in Nash equilibrium on the dense subset.
Similar content being viewed by others
References
Abreu D, Matsushima H (1992) Virtual implementation in iteratively undominated strategies: complete information. Econometrica 60: 993–1008
Abreu D, Sen A (1991) Virtual implementation in Nash equilibrium. Econometrica 59: 997–1021
Dieudonné J (1969) Foundations of modern analysis. Academic Press, New York
Hirsch M (1976) Differential topology. Springer Verlag, Berlin
Maskin E (1977) Nash equilibrium and welfare optimality. Mimeo
Matsushima H (1988) A new approach to the implementation problem. J Econ Theory 45: 128–144
Moore J, Repullo R (1988) Subgame perfect implementation. Econometrica 56: 1191–1220
Palfrey T, Srivastava S (1991) Nash equilibrium using undominated strategies. Econometrica 59: 479–501
Saijo T (1988) Strategy space reduction in Maskin's theorem: sufficient conditions for Nash implementation. Econometrica 56: 693–700
Smale S (1974) Global analysis and economics IIA: extension of a theorem of Debreu. J Math Econ 1: 1–14
Williams S (1984) Sufficient conditions for Nash implementation. Institute for Mathematics and its Applications, University of Minnesota
Author information
Authors and Affiliations
Additional information
The authors thank John Duggan, Ed Green and an anonymous referee for helpful suggestions and comments. Bergin Acknowledges financial support from the Social Sciences and Humanities Research Council of Canada.
Rights and permissions
About this article
Cite this article
Bergin, J., Sen, A. Implementation in generic environments. Soc Choice Welfare 13, 467–478 (1996). https://doi.org/10.1007/BF00182857
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00182857