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Implementation in Adaptive Better-Response Dynamics

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  • Antonio Cabrales

    ()

  • Roberto Serrano

    ()

Abstract

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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Bibliographic Info

Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we075731.

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Date of creation: Jul 2007
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Handle: RePEc:cte:werepe:we075731

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  1. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer, vol. 18(4), pages 655-708.
  2. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  3. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
  4. BERGIN, James & LIPMAN, Bart, 1994. "Evolution with State-Dependent Mutations," CORE Discussion Papers 1994055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Sandholm, William H, 2002. "Evolutionary Implementation and Congestion Pricing," Review of Economic Studies, Wiley Blackwell, vol. 69(3), pages 667-89, July.
  6. Roberto Serrano & Rajiv Vohra, 2002. "A Characterization of Virtual Bayesian Implementation," Economics Working Papers 0028, Institute for Advanced Study, School of Social Science.
  7. Antonio Cabrales & Giovanni Ponti, 1997. "Implementation, elimination of weakly dominated strategies and evolutionary dynamics," Economics Working Papers 221, Department of Economics and Business, Universitat Pompeu Fabra.
  8. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-34, January.
  9. Antonio Cabrales, 1996. "Adaptive dynamics and the implementation problem with complete information," Economics Working Papers 179, Department of Economics and Business, Universitat Pompeu Fabra.
  10. 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.
  11. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
  12. 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.
  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. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Economics Working Papers 0033, Institute for Advanced Study, School of Social Science.
  16. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, December.
  17. Eliaz, K., 1999. "Fault Tolerant Implementation," Papers 21-99, Tel Aviv.
  18. repec:fth:calaec:6-98 is not listed on IDEAS
  19. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  20. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
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