Advanced Search
MyIDEAS: Login

Implementation, Elimination Of Weakly Dominated Strategies And Evolutionary Dynamics

Contents:

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.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-2000-18.pdf
File Function: Fisrt version / Primera version, 2000
Download Restriction: no

Bibliographic Info

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

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

Contact details of provider:
Postal: C/ Guardia Civil, 22, Esc 2a, 1o, E-46020 VALENCIA
Phone: +34 96 319 00 50
Fax: +34 96 319 00 55
Email:
Web page: http://www.ivie.es/
More information through EDIRC

Related research

Keywords: Implementation Theory; Evolutionary Dynamics;

Other versions of this item:

Find related papers by JEL classification:

References

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.:
as in new window
  1. Matthew O. Jackson, 1990. "Undominated Nash Implementation in Bounded Mechanisms," Discussion Papers 966, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Mookherjee, Dilip & Sopher, Barry, 1997. "Learning and Decision Costs in Experimental Constant Sum Games," Games and Economic Behavior, Elsevier, vol. 19(1), pages 97-132, April.
  3. Chen, H.-C. & Friedman, J. W. & Thisse, J.-F., . "Boundedly rational Nash equilibrium: a probabilistic choice approach," CORE Discussion Papers RP -1248, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. A. Roth & I. Er’ev, 2010. "Learning in Extensive Form Games: Experimental Data and Simple Dynamic Models in the Intermediate Run," Levine's Working Paper Archive 387, David K. Levine.
  5. Russell Cooper & Douglas V. DeJong & Thomas W. Ross, 1992. "Cooperation without Reputation: Experimental Evidence from Prisoner's Dilemma Games," Papers 0036, Boston University - Industry Studies Programme.
  6. Cabrales, Antonio, 1999. "Adaptive Dynamics and the Implementation Problem with Complete Information," Journal of Economic Theory, Elsevier, vol. 86(2), pages 159-184, June.
  7. Groves, Theodore & Ledyard, John O, 1977. "Optimal Allocation of Public Goods: A Solution to the "Free Rider" Problem," Econometrica, Econometric Society, vol. 45(4), pages 783-809, May.
  8. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
  9. Ponti, Giovanni, 2000. "Cycles of Learning in the Centipede Game," Games and Economic Behavior, Elsevier, vol. 30(1), pages 115-141, January.
  10. Antonio Cabrales & Gary Charness & Luis Corchón, 1998. "An experiment on Nash implementation," Economics Working Papers 300, Department of Economics and Business, Universitat Pompeu Fabra.
  11. I. Gilboa & A. Matsui, 2010. "Social Stability and Equilibrium," Levine's Working Paper Archive 534, David K. Levine.
  12. Marx, Leslie M. & Swinkels, Jeroen M., 2000. "Order Independence for Iterated Weak Dominance," Games and Economic Behavior, Elsevier, vol. 31(2), pages 324-329, May.
  13. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
  14. Karl H. Schlag, . "Why Imitate, and if so, How? A Bounded Rational Approach to Multi- Armed Bandits," ELSE working papers 028, ESRC Centre on Economics Learning and Social Evolution.
  15. de Trenqualye, Pierre, 1989. "Stable implementation of Lindahl allocations," Economics Letters, Elsevier, vol. 29(4), pages 291-294.
  16. Hofbauer, Josef & Weibull, Jörgen W., 1995. "Evolutionary Selection against Dominated Strategies," Working Paper Series 433, Research Institute of Industrial Economics.
  17. Sjostrom, T., 1991. "Implementation in Undominated Nash Equilibria without Integer Games," Papers 491, Stockholm - International Economic Studies.
  18. T. Börgers, 2010. "Weak Dominance and Approximate Common Knowledge," Levine's Working Paper Archive 378, David K. Levine.
  19. Jordan, J. S., 1986. "Instability in the implementation of Walrasian allocations," Journal of Economic Theory, Elsevier, vol. 39(2), pages 301-328, August.
  20. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
  21. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
  22. R. Cressman & K.H. Schlag, . "The Dynamic (In)Stability of Backwards Induction," ELSE working papers 027, ESRC Centre on Economics Learning and Social Evolution.
  23. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October.
  24. repec:fth:louvco:9644 is not listed on IDEAS
  25. Drew Fudenberg & David Kreps, 2010. "Learning Mixed Equilibria," Levine's Working Paper Archive 415, David K. Levine.
  26. Schlag, Karl H., 1994. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Discussion Paper Serie B 296, University of Bonn, Germany.
  27. De Trenqualye, Pierre, 1988. "Stability of the Groves and Ledyard mechanism," Journal of Economic Theory, Elsevier, vol. 46(1), pages 164-171, October.
  28. Matthew 0. Jackson, 1989. "Implementation in Undominated Strategies - A Look at Bounded Mechanisms," Discussion Papers 833, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  29. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, December.
  30. repec:att:wimass:9529 is not listed on IDEAS
  31. E. Dekel & D. Fudenberg, 2010. "Rational Behavior with Payoff Uncertainty," Levine's Working Paper Archive 379, David K. Levine.
  32. 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).
  33. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
  34. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer, vol. 19(1), pages 59-89.
  35. Binmore, K. & Samuelson, L., 1997. "Evolutionary Drift and Equilibrium Selection," Working papers 9729r, Wisconsin Madison - Social Systems.
  36. Guth, Werner & Schmittberger, Rolf & Schwarze, Bernd, 1982. "An experimental analysis of ultimatum bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 367-388, December.
  37. Vega-Redondo, Fernando, 1989. "Implementation of Lindahl equilibrium: an integration of the static and dynamic approaches," Mathematical Social Sciences, Elsevier, vol. 18(3), pages 211-228, December.
  38. 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.
  39. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
  40. repec:fth:calaec:16-97 is not listed on IDEAS
  41. Walker, Mark, 1981. "A Simple Incentive Compatible Scheme for Attaining Lindahl Allocations," Econometrica, Econometric Society, vol. 49(1), pages 65-71, January.
  42. repec:att:wimass:9325 is not listed on IDEAS
  43. Walker, Mark, 1984. "A simple auctioneerless mechanism with Walrasian properties," Journal of Economic Theory, Elsevier, vol. 32(1), pages 111-127, February.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Sandholm,W.H., 1999. "Evolutionary implementation and congestion pricing," Working papers 38, Wisconsin Madison - Social Systems.
  2. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science.
  3. 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).
  4. Jordi Brandts & Antonio Cabrales & Gary Charness, 2007. "Forward induction and entry deterrence: an experiment," Economic Theory, Springer, vol. 33(1), pages 183-209, October.
  5. Antonio Cabrales & Roberto Serrano, 2007. "Implementation in Adaptive Better-Response Dynamics," Economics Working Papers we075731, Universidad Carlos III, Departamento de Economía.
  6. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics.
  7. 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.
  8. Marco Galbiati, 2006. "Fair Divisions as Attracting Nash Equilibria of Simple Games," Economics Working Papers ECO2006/24, European University Institute.
  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. Giovanni Ponti & Anita Gantner & Dunia López-Pintado & Robert Montgomery, 2003. "Solomon's Dilemma: An experimental study on dynamic implementation," Review of Economic Design, Springer, vol. 8(2), pages 217-239, October.
  11. David K Levine & Aldo Rustichini, 2000. "Introduction: The Dynamic Games Special Issue," Levine's Working Paper Archive 2127, David K. Levine.
  12. Sandholm,W.H., 2001. "Negative externalities and evolutionary implementation," Working papers 15, Wisconsin Madison - Social Systems.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:ivi:wpasad:2000-18. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Departamento de Edición).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.