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Rationalizable Implementation

Listed author(s):
  • Dirk Bergemann
  • Stephen Morris
  • Olivier Tercieux

We consider the implementation of social choice functions under complete information in rationalizable strategies. A strict (and thus stronger) version of the monotonicity condition introduced by Maskin (1999) is necessary under the solution concept of rationalizability. Assuming the social choice function is responsive (i.e., it never selects the same outcome in two distinct states), we show that it is also sufficient under a mild "no worst alternative" condition. In particular, no economic condition is required. We also discuss how our results extend when the social choice function is not responsive.

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 661465000000000022.

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Date of creation: 17 Mar 2010
Handle: RePEc:cla:levarc:661465000000000022
Contact details of provider: Web page: http://www.dklevine.com/

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  1. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-134, January.
  2. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
  3. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
  4. Bergemann, Dirk & Morris, Stephen & Tercieux, Olivier, 2011. "Rationalizable implementation," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1253-1274, May.
  5. Georgy Artemov & Takashi Kunimoto & Roberto Serrano, 2007. "Robust virtual implementation with incomplete information: Towards a reinterpretation of the Wilson doctrine," Working Papers 2007-14, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  6. Bergemann, Dirk & Morris, Stephen, 2011. "Robust implementation in general mechanisms," Games and Economic Behavior, Elsevier, vol. 71(2), pages 261-281, March.
  7. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
  8. Benoît, Jean-Pierre & Ok, Efe A., 2008. "Nash implementation without no-veto power," Games and Economic Behavior, Elsevier, vol. 64(1), pages 51-67, September.
  9. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 111-125, January.
  10. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October.
  11. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
  12. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-477, March.
  13. Roberto Serrano & Antonio Cabrales, 2007. "Implementation in Adaptive Better-Response Dynamics," Working Papers 2007-10, Brown University, Department of Economics.
  14. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288 Elsevier.
  15. Dirk Bergemann & Stephen Morris, 2009. "Robust Implementation in Direct Mechanisms," Review of Economic Studies, Oxford University Press, vol. 76(4), pages 1175-1204.
  16. Serrano, Roberto & Vohra, Rajiv, 2010. "Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 775-785, September.
  17. Marion Oury & Olivier Tercieux, 2012. "Continuous Implementation," Econometrica, Econometric Society, vol. 80(4), pages 1605-1637, 07.
  18. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
  19. Lipman Barton L., 1994. "A Note on the Implications of Common Knowledge of Rationality," Games and Economic Behavior, Elsevier, vol. 6(1), pages 114-129, January.
  20. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, vol. 60(6), pages 1439-1442, November.
  21. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
  22. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57 World Scientific Publishing Co. Pte. Ltd..
  23. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
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