IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

Implementation, Elimination of Weakly Dominated Strategies and Evolotionary Dynamics

  • Antonio Cabrales
  • Giovanni Ponti

This paper is concerned with the realism of mechanisms that implement social choice functions in the traditional sense. Will agents actually play the equilibrium assumed by the analysis? As an example, we study convergence and stability prop-erties of Sjostrom's (1994) mechanism, on the assumption that boundedly rational players find their way to equilibrium using monotonic learning dynamics. This mechanism implements most social choice functions in economic environments using as a solution concept the iterated elimination of weakly dominated strategies (only one round of deletion of weakly dominated strategies is needed). There are, how-ever, many sets of Nash equilibria whose payoffs may be very different from those desired by the social choice function. We show that many equilibria in all the sets of equilibria we have described are the limit points of trajectories that have completely mixed initial conditions. The initial conditions that lead to these equilibria need not be very close to the limiting point. Furthermore, even if the dynamics converge to the "right" set of equilibria, it still can converge to quite a poor outcome in welfare terms.

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: ftp://ftp.repec.org/RePEc/els/esrcls/weak.pdf
Download Restriction: no

Paper provided by ESRC Centre on Economics Learning and Social Evolution in its series ELSE working papers with number 057.

as
in new window

Length:
Date of creation:
Date of revision:
Handle: RePEc:els:esrcls:057
Contact details of provider: Web page: http://else.econ.ucl.ac.uk/
Email:


More information through EDIRC

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. Antonio Cabrales, 1996. "Adaptive dynamics and the implementation problem with complete information," Economics Working Papers 179, Department of Economics and Business, Universitat Pompeu Fabra.
  2. Sjostrom, T., 1991. "Implementation in Undominated Nash Equilibria without Integer Games," Papers 491, Stockholm - International Economic Studies.
  3. Samuelson, L. & Zhang, J., 1991. "Evolutionary Stability in Asymmetric Games," Papers 9132, Tilburg - Center for Economic Research.
  4. de Trenqualye, Pierre, 1989. "Stable implementation of Lindahl allocations," Economics Letters, Elsevier, vol. 29(4), pages 291-294.
  5. Fudenberg, D. & Kreps, D.M., 1992. "Learning Mixed Equilibria," Working papers 92-13, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. Hofbauer, Josef & Weibull, Jorgen W., 1996. "Evolutionary Selection against Dominated Strategies," Journal of Economic Theory, Elsevier, vol. 71(2), pages 558-573, November.
  7. Barry Sopher & Dilip Mookherjee, 2000. "Learning and Decision Costs in Experimental Constant Sum Games," Departmental Working Papers 199625, Rutgers University, Department of Economics.
  8. Ponti, Giovanni, 2000. "Cycles of Learning in the Centipede Game," Games and Economic Behavior, Elsevier, vol. 30(1), pages 115-141, January.
  9. 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.
  10. 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.
  11. Matthew O. Jackson, 1990. "Undominated Nash Implementation in Bounded Mechanisms," Discussion Papers 966, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  12. Cooper, Russell & DeJong, Douglas V. & Forsythe, Robert & Ross, Thomas W., 1996. "Cooperation without Reputation: Experimental Evidence from Prisoner's Dilemma Games," Games and Economic Behavior, Elsevier, vol. 12(2), pages 187-218, February.
  13. Drew Fudenberg & Eddie Dekel, 1987. "Rational Behavior with Payoff Uncertainty," Working papers 471, Massachusetts Institute of Technology (MIT), Department of Economics.
  14. Theodore Groves & John Ledyard, 1976. "Optimal Allocation of Public Goods: A Solution to the 'Free Rider Problem'," Discussion Papers 144, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  15. De Trenqualye, Pierre, 1988. "Stability of the Groves and Ledyard mechanism," Journal of Economic Theory, Elsevier, vol. 46(1), pages 164-171, October.
  16. Jordan, J. S., 1986. "Instability in the implementation of Walrasian allocations," Journal of Economic Theory, Elsevier, vol. 39(2), pages 301-328, August.
  17. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
  18. Borgers Tilman, 1994. "Weak Dominance and Approximate Common Knowledge," Journal of Economic Theory, Elsevier, vol. 64(1), pages 265-276, October.
  19. Cressman, R. & Schlag, K. H., 1998. "The Dynamic (In)Stability of Backwards Induction," Journal of Economic Theory, Elsevier, vol. 83(2), pages 260-285, December.
  20. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
  21. CHEN, Hsiao-Ch. & FRIEDMAN, J.W. & THISSE, Jacques-Francois, 1996. "Boundedly Rational Nash Equilibrium: A Probabilistic Choice Approach," CORE Discussion Papers 1996044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  22. 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).
  23. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-67, May.
  24. 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.
  25. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October.
  26. T. Borgers & R. Sarin, 2010. "Learning Through Reinforcement and Replicator Dynamics," Levine's Working Paper Archive 380, David K. Levine.
  27. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
  28. K. Schlag, 2010. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Levine's Working Paper Archive 454, David K. Levine.
  29. Yan Chen & Fang-Fang Tang, 1998. "Learning and Incentive-Compatible Mechanisms for Public Goods Provision: An Experimental Study," Journal of Political Economy, University of Chicago Press, vol. 106(3), pages 633-662, June.
  30. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, March.
  31. Binmore, K. & Samuelson, L. & Gale, J., 1993. "Learning to be Imperfect: The Ultimatum Game," Working papers 9325, Wisconsin Madison - Social Systems.
  32. repec:cdl:ucsbec:16-97 is not listed on IDEAS
  33. Binmore, K. & Samuelson, L., 1997. "Evolutionary Drift and Equilibrium Selection," Working papers 9729r, Wisconsin Madison - Social Systems.
  34. Cressman, R., 1996. "Evolutionary Stability in the Finitely Repeated Prisoner 's Dilemma Game," Journal of Economic Theory, Elsevier, vol. 68(1), pages 234-248, January.
  35. Cabrales, Antonio & Charness, Gary & Corchon, Luis C., 2003. "An experiment on Nash implementation," Journal of Economic Behavior & Organization, Elsevier, vol. 51(2), pages 161-193, June.
  36. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
  37. Walker, Mark, 1981. "A Simple Incentive Compatible Scheme for Attaining Lindahl Allocations," Econometrica, Econometric Society, vol. 49(1), pages 65-71, January.
  38. 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.
  39. 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.
  40. Matthew O. Jackson, 1992. "Implementation in Undominated Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Oxford University Press, vol. 59(4), pages 757-775.
  41. Walker, Mark, 1984. "A simple auctioneerless mechanism with Walrasian properties," Journal of Economic Theory, Elsevier, vol. 32(1), pages 111-127, February.
  42. 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.
  43. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 59-89.
Full references (including those not matched with items on IDEAS)

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

When requesting a correction, please mention this item's handle: RePEc:els:esrcls:057. 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: (s. malkani)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.