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Implementation, Elimination Of Weakly Dominated Strategies And Evolutionary Dynamics

  • Antonio Cabrales

    (Universitat Pompeu Fabra)

  • Giovanni Ponti

    (Universidad de Alicante)

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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File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-2000-18.pdf
File Function: Fisrt version / Primera version, 2000
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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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  13. Itzhak Gilboa & Akihiko Matsui, 1991. "Social Stability and Equilibrium," Post-Print hal-00753235, HAL.
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  29. Tang, Fang-Fang, 1996. "Anticipatory Learning in Two-Person Games: An Experimental Study, Part II. Learning," Discussion Paper Serie B 363, University of Bonn, Germany.
  30. 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).
  31. de Trenqualye, Pierre, 1989. "Stable implementation of Lindahl allocations," Economics Letters, Elsevier, vol. 29(4), pages 291-294.
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  42. repec:cdl:ucsbec:16-97 is not listed on IDEAS
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