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Implementation in Adaptive Better-Response Dynamics

We study the classic implementation problem under the behavioral assumption that agents myopically adjust their actions in the direction of better-responses within a given institution. We offer results both under complete and incomplete information. First, we show that a necessary condition for assymptotically stable implementation is a small variation of (Maskin) monotonicity, which we call quasimonotonicity. Under standard assumptions in economic environments, we also provide a mechanism for Nash implementation which has good dynamic properties if the rule is quasimonotonic. Thus, quasimonotonicity is both necessary and almost sufficient for assymptotically stable implementation. Under incomplete information, incentive compatibility is necessary for any kind of stable implementation in our sense, while Bayesian quasimonotonicity is necessary for assymptotically stable implementation. Both conditions are also essentially sufficient for assymptotically stable implementation. We then tighten the assumptions on preferences and mutation processes and provide mechanisms for stochastically stable implementation under more permissive conditions on social choice rules.

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Paper provided by Brown University, Department of Economics in its series Working Papers with number 2007-10.

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Date of creation: 2007
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Handle: RePEc:bro:econwp:2007-10
Contact details of provider: Postal: Department of Economics, Brown University, Providence, RI 02912

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  1. Maskin, Eric & Sjostrom, Tomas, 2001. "Implementation Theory," Working Papers 5-01-1, Pennsylvania State University, Department of Economics.
  2. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
  3. Antonio Cabrales & Giovanni Ponti, 2000. "Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 247-282, April.
  4. J Bergin & B L Lipman, 1997. "Evolution with state-dependent Mutations," Levine's Working Paper Archive 771, David K. Levine.
  5. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, June.
  6. Eliaz, K., 1999. "Fault Tolerant Implementation," Papers 21-99, Tel Aviv.
  7. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
  8. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  9. Jackson, Matthew O., 1999. "A Crash Course in Implementation Theory," Working Papers 1076, California Institute of Technology, Division of the Humanities and Social Sciences.
  10. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Economics Working Papers 0033, Institute for Advanced Study, School of Social Science.
  11. Serrano, Roberto & Vohra, Rajiv, 2005. "A characterization of virtual Bayesian implementation," Games and Economic Behavior, Elsevier, vol. 50(2), pages 312-331, February.
  12. Sandholm, William H, 2002. "Evolutionary Implementation and Congestion Pricing," Review of Economic Studies, Wiley Blackwell, vol. 69(3), pages 667-89, July.
  13. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
  14. Sjostrom Tomas, 1994. "Implementation in Undominated Nash Equilibria without Integer Games," Games and Economic Behavior, Elsevier, vol. 6(3), pages 502-511, May.
  15. Antonio Cabrales, 1996. "Adaptive dynamics and the implementation problem with complete information," Economics Working Papers 179, Department of Economics and Business, Universitat Pompeu Fabra.
  16. Palfrey, Thomas R., 2002. "Implementation theory," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 61, pages 2271-2326 Elsevier.
  17. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
  18. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  19. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-34, January.
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