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Implementation in Adaptive Better-Response Dynamics

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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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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

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Postal: Department of Economics, Brown University, Providence, RI 02912

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  1. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Economics Working Papers, Institute for Advanced Study, School of Social Science 0033, Institute for Advanced Study, School of Social Science.
  2. Cabrales, Antonio, 1999. "Adaptive Dynamics and the Implementation Problem with Complete Information," Journal of Economic Theory, Elsevier, Elsevier, vol. 86(2), pages 159-184, June.
  3. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262061945, December.
  4. J. Bergin & B. Lipman, 2010. "Evolution with State-Dependent Mutations," Levine's Working Paper Archive 486, David K. Levine.
  5. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 66(1), pages 23-38, January.
  6. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare, Elsevier, 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.
  7. Sjostrom, T., 1991. "Implementation in Undominated Nash Equilibria without Integer Games," Papers, Stockholm - International Economic Studies 491, Stockholm - International Economic Studies.
  8. Antonio Cabrales & Giovanni Ponti, 2000. "Implementation, Elimination Of Weakly Dominated Strategies And Evolutionary Dynamics," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 2000-18, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  9. Palfrey, Thomas R., 2002. "Implementation theory," Handbook of Game Theory with Economic Applications, Elsevier, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 61, pages 2271-2326 Elsevier.
  10. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, Elsevier, vol. 39(1), pages 14-33, June.
  11. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, Econometric Society, vol. 61(1), pages 29-56, January.
  12. Sandholm, William H, 2002. "Evolutionary Implementation and Congestion Pricing," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 69(3), pages 667-89, July.
  13. Jackson, Matthew O., 1999. "A Crash Course in Implementation Theory," Working Papers, California Institute of Technology, Division of the Humanities and Social Sciences 1076, California Institute of Technology, Division of the Humanities and Social Sciences.
  14. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 461-77, March.
  15. Roberto Serrano & Rajiv Vohra, 2002. "A Characterization of Virtual Bayesian Implementation," Working Papers, Brown University, Department of Economics 2002-11, Brown University, Department of Economics.
  16. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262731215, December.
  17. Eliaz, Kfir, 2002. "Fault Tolerant Implementation," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 69(3), pages 589-610, July.
  18. repec:fth:calaec:6-98 is not listed on IDEAS
  19. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, Econometric Society, vol. 61(1), pages 57-84, January.
  20. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, Econometric Society, vol. 57(1), pages 115-34, January.
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