Social Choice and Welfare

, Volume 8, Issue 3, pp 235–245 | Cite as

Strategy space reduction for feasible implementation of Walrasian performance

  • B. Chakravorti
Article

Abstract

The purpose of this paper is to establish a new upper bound on the size of the strategy space that is needed to feasibly implement the constrained Walrasian correspondence (W). This bound is significantly lower than those available from the literature on feasible Nash-implementation. Our focus on W has wider implications since implementation of W implies partial implementation of “almost” all individually rational and efficient implementable economic performance standards. Hence, our results provide a parallel — in the economic context — to the research agenda of Saijo [13] and McKelvey [9] who have established new upper bounds on the size of the strategy space required for feasible implementation of Nash-implementable performance standards in general social choice contexts. We prove that it is sufficient to have only three agents in an economy who make price-related announcements. This is a critical source of the reduction in strategy space.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chakravorti B (1991) Communication requirements and strategic mechanisms for market organization. J Math Econ 20: 35–47Google Scholar
  2. 2.
    Debreu G (1959) The theory of value. Wiley, New YorkGoogle Scholar
  3. 3.
    Hurwicz L (1977) On the dimensional requirements of Pareto-satisfactory processes. In: Arrow K, Hurwicz L (eds) Studies in resource allocation processes. Cambridge University Press, CambridgeGoogle Scholar
  4. 4.
    Hurwicz L (1979) On allocations attainable through Nash equilibria. J Econ Theory 21: 140–165Google Scholar
  5. 5.
    Hurwicz L, Maskin E, Postlewaite A (1984) Feasible implementation of social choice correspondences, mimeo, University of MinnesotaGoogle Scholar
  6. 6.
    Marschak T (1986) Organization design. In: Arrow K, Intriligator M (eds) Handbook of mathematical economics, Vol III. North-Holland, AmsterdamGoogle Scholar
  7. 7.
    Maskin E (1977) Nash equilibrium and welfare optimality, mimeo, MITGoogle Scholar
  8. 8.
    Maskin E (1985) The theory of implementation in Nash equilibrium: a survey. In: Hurwicz L, Schmeidler D, Sonnenschein H (eds) Social goals and social organization: essays in memory of Elisha Pazner. Cambridge University Press, CambridgeGoogle Scholar
  9. 9.
    McKelvey R (1989) Game forms for Nash implementation of general social choice correspondences. Soc Choice Welfare 6: 139–156Google Scholar
  10. 10.
    Mount K, and Reiter S (1974) The informational size of message spaces. J Econ Theory 8: 161–192Google Scholar
  11. 11.
    Reichelstein S, Reiter S (1988) Game forms with minimal strategy spaces. Econometrica 56: 661–692Google Scholar
  12. 12.
    Saijo T (1986) The strategy space required for implementation is twice that required for realization, mimeo, University of California, Santa BarbaraGoogle Scholar
  13. 13.
    Saijo T (1988) Strategy space reduction in Maskin's theorem: sufficient conditions for Nash implementation. Enonometrica 56: 693–700Google Scholar
  14. 14.
    Thomson W (1984) The manipulability of resource allocation mechanisms. Rev Econ Stud 51: 447–460Google Scholar

Copyright information

© Spring-Verlag 1991

Authors and Affiliations

  • B. Chakravorti
    • 1
  1. 1.Department of EconomicsUniversity of Illinois at Urbana-ChampaignChampaignUSA

Personalised recommendations