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Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics

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  • Antonio Cabrales

    (Universitat Pompeu Fabra and ELSE)

  • Giovanni Ponti

    (Universidad de Alicante and ELSE)

Abstract

This paper studies convergence and stability properties of Sjostrom's (1994) mechanism, under the assumption that boundedly rational players find their way to equilibrium using monotonic evolutionary dynamics and best-reply dynamics. This mechanism implements most social choice functions in economic environments using as a solution concept one round of deletion of weakly dominated strategies and one round of deletion of strictly dominated strategies. However, there are other sets of Nash equilibrium, whose payoffs may be very different from those desired by the social choice function. With monotonic dynamics, all these sets of equilibrium contain limit points of the evolutionary dynamics. Furthermore, even if the dynamics converge to the "right" set of equilibria (i.e., the one which contains the solution of the mechanism), it may converge to an equilibrium which is worse in welfare terms. In contrast with this result, any interior solution of the best-reply dynamics converges to the equilibrium whose outcome the planner desires. (Copyright: Elsevier)

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File URL: http://dx.doi.org/10.1006/redy.1999.0082
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Bibliographic Info

Article provided by Elsevier for the Society for Economic Dynamics in its journal Review of Economic Dynamics.

Volume (Year): 3 (2000)
Issue (Month): 2 (April)
Pages: 247-282

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Handle: RePEc:red:issued:v:3:y:2000:i:2:p:247-282

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Citations

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Cited by:
  1. Roberto Serrano & Antonio Cabrales, 2007. "Implemetation In Adaptive Better-Response Dynamics," Working Papers wp2007_0708, CEMFI.
  2. Dunia López-Pintado & Giovanni Ponti, 2003. "Solomon'S Dilemma: An Experimental Study On Dynamic Implementation," Working Papers. Serie AD 2003-11, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  3. Galbiati, Marco, 2008. "Fair divisions as attracting Nash equilibria of simple games," Economics Letters, Elsevier, vol. 100(1), pages 72-75, July.
  4. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Economics Working Papers 0033, Institute for Advanced Study, School of Social Science.
  5. Timothy N. Cason & Tatsuyoshi Saijo & Tomas Sjostrom & Takehiko Yamato, 2005. "Secure Implementation Experiments: Do Strategy-proof Mechanisms Really Work?," Economics Working Papers 0055, Institute for Advanced Study, School of Social Science.
  6. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science.
  7. Sandholm,W.H., 2001. "Negative externalities and evolutionary implementation," Working papers 15, Wisconsin Madison - Social Systems.
  8. Jordi Brandts & Antonio Cabrales & Gary Charness, 2007. "Forward induction and entry deterrence: an experiment," Economic Theory, Springer, vol. 33(1), pages 183-209, October.
  9. David K. Levine & Aldo Rustichini, 2000. "Introduction," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 213-215, April.
  10. David K Levine & Aldo Rustichini, 2000. "Introduction: The Dynamic Games Special Issue," Levine's Working Paper Archive 2127, David K. Levine.
  11. Norovsambuu Tumennasan, 2011. "To Err is Human: Implementation in Quantal Response Equilibria," Economics Working Papers 2011-11, School of Economics and Management, University of Aarhus.
  12. Sandholm,W.H., 1999. "Evolutionary implementation and congestion pricing," Working papers 38, Wisconsin Madison - Social Systems.

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