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Credible Implementation

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  • Chakravorti, B.
  • Corchon, L.C.

Abstract

The theory of mechanism design and implementation abounds with clever mechanisms whose equilibrium outcomes are optimal according to some social choice rule. However, the cleverness of these mechanisms relies on intricate systems of rewards and punishments off-the-equilibrium path. Generally, it is not in the designer's best interest to go through with the reward/punishment in the "subgame" arising from some disequilibrium play. This would make the mechanism's outcome function non-credible. In the context of exchange economies, we define an appropiate notion of "credible" implementation and show that (a) the non-dictatorial Pareto correspondence can be crediblyimplemented (b) there exists no credibly implementable Pareto-efficient and individually rational social choice rule and (c) there exists no credibly implementable fair social choice rules. We derive necessary and sufficient conditions for credible implementability of choice rules. The main implication is paradoxical: it is suboptimal for the designer to be endowed with "too much" information about the economy. Finally, we show that the negative results persist even under weaker credibility requirements .

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Bibliographic Info

Paper provided by Bell Communications - Economic Research Group in its series Papers with number 76.

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Length: 28 pages
Date of creation: 1992
Date of revision:
Handle: RePEc:fth:bellco:76

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Postal: Bell Communications Research; Economic Research Group, 445 South street Morristown, NJ 07962-1910, USA

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Keywords: economic equilibrium ; game theory;

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References

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  1. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 23-38, January.
  2. Luis Corchón & Sandeep Baliga & Tomas Sjöström, 1995. "The Theory Of Implementation When The Planner Is A Player," Working Papers. Serie AD 1995-14, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  3. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
  4. Mathias Dewatripont & Philippe Aghion & Patrick Rey, 1994. "Renegotiation design with unverifiable information," ULB Institutional Repository 2013/9591, ULB -- Universite Libre de Bruxelles.
  5. Jackson, Matthew O. & Palfrey, Thomas R., 1999. "Voluntary Implementation," Working Papers 1077, California Institute of Technology, Division of the Humanities and Social Sciences.
  6. Cho, In-Koo & Kreps, David M, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, MIT Press, vol. 102(2), pages 179-221, May.
  7. Rubinstein, Ariel & Wolinsky, Asher, 1992. "Renegotiation-Proof Implementation and Time Preferences," American Economic Review, American Economic Association, vol. 82(3), pages 600-614, June.
  8. Antonio Villar Notario & Carmen Herrero Blanco, 1990. "Vector mappings with diagonal images," Working Papers. Serie AD 1990-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  9. Matthew O. Jackson, 1990. "Undominated Nash Implementation in Bounded Mechanisms," Discussion Papers 966, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Chakravorti, Bhaskar, 1993. "Sequential rationality, implementation and pre-play communication," Journal of Mathematical Economics, Elsevier, vol. 22(3), pages 265-294.
  11. Mirman, Leonard J & Samuelson, Larry & Urbano, Amparo, 1993. "Monopoly Experimentation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(3), pages 549-63, August.
  12. Palfrey, Thomas R & Srivastava, Sanjay, 1991. "Nash Implementation Using Undominated Strategies," Econometrica, Econometric Society, vol. 59(2), pages 479-501, March.
  13. Hurwicz, L, 1979. "Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 217-25, April.
  14. Debraj Ray & Kaoru Ueda, 1996. "Egalitarianism and Incentives," Boston University - Institute for Economic Development 73, Boston University, Institute for Economic Development.
  15. Aghion, Philippe & Dewatripont, Mathias & Rey, Patrick, 1994. "Renegotiation Design with Unverifiable Information," Scholarly Articles 12375014, Harvard University Department of Economics.
  16. Sandeep Baliga & Tomas Sjostrom, 1996. "Interactive Implementation," Harvard Institute of Economic Research Working Papers 1751, Harvard - Institute of Economic Research.
  17. Palfrey, Thomas R & Srivastava, Sanjay, 1987. "On Bayesian Implementable Allocations," Review of Economic Studies, Wiley Blackwell, vol. 54(2), pages 193-208, April.
  18. Thomson, William, 1984. "The Manipulability of Resource Allocation Mechanisms," Review of Economic Studies, Wiley Blackwell, vol. 51(3), pages 447-60, July.
  19. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
  20. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
  21. Chakravorti, Bhaskar, 1992. "Efficiency and Mechanisms with No Regret," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 45-59, February.
  22. Marhuenda, F, 1995. "Distribution of Income and Aggregation of Demand," Econometrica, Econometric Society, vol. 63(3), pages 647-66, May.
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Citations

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Cited by:
  1. Matthew O. Jackson & Thomas R. Palfrey, 1997. "Efficiency and Voluntary Implementation in Markets with Repeated Pairwise Bargaining," Game Theory and Information 9711003, EconWPA.
  2. Amoros, Pablo, 2004. "Nash implementation and uncertain renegotiation," Games and Economic Behavior, Elsevier, vol. 49(2), pages 424-434, November.
  3. John Conley & Simon Wilkie, 1994. "Implementing the nash extension bargaining solution for non-convex problems," Review of Economic Design, Springer, vol. 1(1), pages 205-216, December.
  4. Luis C. Corchon, 2007. "The theory of implementation : what did we learn?," Economics Working Papers we081207, Universidad Carlos III, Departamento de Economía.
  5. Jackson, Matthew O., 1999. "A Crash Course in Implementation Theory," Working Papers 1076, California Institute of Technology, Division of the Humanities and Social Sciences.

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