Implemetation In Adaptive Better-Response Dynamics

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Implemetation In Adaptive Better-Response Dynamics

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Roberto Serrano ()
Antonio Cabrales () (CEMFI, Centro de Estudios Monetarios y Financieros)

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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 CEMFI in its series Working Papers with number wp2007_0708.

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Date of creation: Jul 2007
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Handle: RePEc:cmf:wpaper:wp2007_0708

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Paper
- Antonio Cabrales & Roberto Serrano, 2007. "Implementation in Adaptive Better-Response Dynamics," Economics Working Papers we075731, Universidad Carlos III, Departamento de Economía. [Downloadable!]
- Roberto Serrano & Antonio Cabrales, 2007. "Implementation in Adaptive Better-Response Dynamics," Working Papers 2007-10, Brown University, Department of Economics. [Downloadable!]
- Antonio Cabrales & Roberto Serrano, 2007. "Implementation in adaptive better-response dynamics," Working Papers 2007-16, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales. [Downloadable!]

Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy-Making and Implementation

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-34, January. [Downloadable!] (restricted)
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. [Downloadable!] (restricted)
Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June. [Downloadable!] (restricted)
Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-56, July. [Downloadable!] (restricted)
Other versions:
- BERGINÊ, James & LIPMAN, Bart, 1994. "Evolution with State-Dependent Mutations," CORE Discussion Papers 1994055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
Serrano, Roberto & Vohra, Rajiv, 2005. "A characterization of virtual Bayesian implementation," Games and Economic Behavior, Elsevier, vol. 50(2), pages 312-331, February. [Downloadable!] (restricted)
Other versions:
- Roberto Serrano & Rajiv Vohra, 2002. "A Characterization of Virtual Bayesian Implementation," Working Papers 2002-11, Brown University, Department of Economics. [Downloadable!]
- Roberto Serrano & Rajiv Vohra, 2002. "A Characterization of Virtual Bayesian Implementation," Economics Working Papers 0028, Institute for Advanced Study, School of Social Science. [Downloadable!]
Sjostrom Tomas, 1994. "Implementation in Undominated Nash Equilibria without Integer Games," Games and Economic Behavior, Elsevier, vol. 6(3), pages 502-511, May. [Downloadable!] (restricted)
Other versions:
- Sjostrom, T., 1991. "Implementation in Undominated Nash Equilibria without Integer Games," Papers 491, Stockholm - International Economic Studies.
Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January. [Downloadable!] (restricted)
Other versions:
- Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Economics Working Papers 0033, Institute for Advanced Study, School of Social Science. [Downloadable!]
Other versions:
- Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics. [Downloadable!]
Sandholm, William H, 2002. "Evolutionary Implementation and Congestion Pricing," Review of Economic Studies, Blackwell Publishing, vol. 69(3), pages 667-89, July.
Eliaz, Kfir, 2002. "Fault Tolerant Implementation," Review of Economic Studies, Blackwell Publishing, vol. 69(3), pages 589-610, July.
Other versions:
- Eliaz, K., 1999. "Fault Tolerant Implementation," Papers 21-99, Tel Aviv.
Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Blackwell Publishing, vol. 66(1), pages 23-38, January. [Downloadable!] (restricted)
Other versions:
- Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March. [Downloadable!] (restricted)
Cabrales, Antonio, 1999. "Adaptive Dynamics and the Implementation Problem with Complete Information," Journal of Economic Theory, Elsevier, vol. 86(2), pages 159-184, June. [Downloadable!] (restricted)
Other versions:
- Antonio Cabrales, 1996. "Adaptive Dynamics and the Implementation Problem with Complete Information," Economics Working Papers 179, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
- Antonio Cabrales, . "Adaptive Dynamics and the Implementation Problem with Complete Information," ELSE working papers 009, ESRC Centre on Economics Learning and Social Evolution. [Downloadable!]
Antonio Cabrales & Giovanni Ponti, 2000. "Implementation, Elimination Of Weakly Dominated Strategies And Evolutionary Dynamics," Working Papers. Serie AD 2000-18, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
Other versions:
- Antonio Cabrales & Giovanni Ponti, . "Implementation, Elimination of Weakly Dominated Strategies and Evolotionary Dynamics," ELSE working papers 057, ESRC Centre on Economics Learning and Social Evolution. [Downloadable!]
- 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. [Downloadable!]
- Antonio Cabrales & Giovanni Ponti, . "Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics," University of California at Santa Barbara, Economics Working Paper Series 6-98, Department of Economics, UC Santa Barbara.
- 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. [Downloadable!] (restricted)
Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January. [Downloadable!] (restricted)
Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer, vol. 18(4), pages 655-708. [Downloadable!] (restricted)
Other versions:
- Jackson, Matthew O., 1999. "A Crash Course in Implementation Theory," Working Papers 1076, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine. [Downloadable!]
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. [Downloadable!] (restricted)
Other versions:
- Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science. [Downloadable!]
- Maskin, Eric & Sjostrom, Tomas, 2001. "Implementation Theory," Working Papers 5-01-1, Pennsylvania State University, Department of Economics. [Downloadable!]

Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

Saran, Rene, 2008. "The Maximal Domain for the Revelation Principle when Preferences are Menu Dependent," Research Memoranda 023, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]

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