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Implementation, Elimination Of Weakly Dominated Strategies And Evolutionary Dynamics

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Author Info

  • Antonio Cabrales

    (Universitat Pompeu Fabra)

  • Giovanni Ponti

    (Universidad de Alicante)

Abstract

This paper studies convergence and stability properties of Sjöström's (1994) mechanism, under the assumption that boundedly rational players find their way to equilibrium using monotonic learning 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 equilibria, whose payoffs may be very different from those desired by the social choice function. With monotonic dynamics, all these sets of equilibria contain limit points of the learning 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.

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Bibliographic Info

Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 2000-18.

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Length: 37 pages
Date of creation: Oct 2000
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:2000-18

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Keywords: Implementation Theory; Evolutionary Dynamics;

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References

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Citations

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Cited by:
  1. Marco Galbiati, 2006. "Fair Divisions as Attracting Nash Equilibria of Simple Games," Economics Working Papers ECO2006/24, European University Institute.
  2. 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.
  3. Antonio Cabrales & Roberto Serrano, 2007. "Implementation in adaptive better-response dynamics," Working Papers 2007-16, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  4. Tatsuyoshi Saijo & Timothy N. Cason & Tomas Sjostrom, 2003. "Secure Implementation Experiments:Do Strategy-proof Mechanisms Really Work?," Discussion papers 03012, Research Institute of Economy, Trade and Industry (RIETI).
  5. David K Levine & Aldo Rustichini, 2000. "Introduction: The Dynamic Games Special Issue," Levine's Working Paper Archive 2127, David K. Levine.
  6. 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.
  7. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics.
  8. 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).
  9. Tumennasan, Norovsambuu, 2013. "To err is human: Implementation in quantal response equilibria," Games and Economic Behavior, Elsevier, vol. 77(1), pages 138-152.
  10. Sandholm,W.H., 1999. "Evolutionary implementation and congestion pricing," Working papers 38, Wisconsin Madison - Social Systems.
  11. Sandholm,W.H., 2001. "Negative externalities and evolutionary implementation," Working papers 15, Wisconsin Madison - Social Systems.
  12. Jordi Brandts & Antonio Cabrales & Gary Charness, 2007. "Forward induction and entry deterrence: an experiment," Economic Theory, Springer, vol. 33(1), pages 183-209, October.

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