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Virtual Implementation in Nash Equilibrium


  • Abreu, Dilip
  • Sen, Arunava


Consider a social choice correspondence as a mapping from preference profiles to lotteries over some finite set of alternatives. A virtually implementable social choice function in Nash equilibrium is defined, under mild domain restrictions it is shown that in societies with at least three individuals all social choice correspondences are virtually implementable in Nash equilibrium. This contrasts with Maskin's classic characterization, which requires monotonicity as a necessary condition for exact implementation in Nash equilibrium. The two person case is considered seperately. While not all two-person social choice functions are virtually implementable, our necessary and sufficient condition is simple, which contrasts with the complex necessary and sufficient conditions for exact implementation. Copyright 1991 by The Econometric Society.

Suggested Citation

  • Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
  • Handle: RePEc:ecm:emetrp:v:59:y:1991:i:4:p:997-1021

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    References listed on IDEAS

    1. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    2. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339 Elsevier.
    3. repec:cup:etheor:v:13:y:1997:i:5:p:615-45 is not listed on IDEAS
    4. Peter C.B. Phillips, 1998. "Econometric Analysis of Fisher's Equation," Cowles Foundation Discussion Papers 1180, Cowles Foundation for Research in Economics, Yale University.
    5. Bergstrom, A. R., 1988. "The History of Continuous-Time Econometric Models," Econometric Theory, Cambridge University Press, vol. 4(03), pages 365-383, December.
    6. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
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