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Implementation, elimination of weakly dominated strategies and evolutionary 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 the convergence and stability properties of Sj\"ostr\"om's (1994) mechanism, on the assumption that boundedly rational players find their way to equilibrium using monotonic learning dynamics and also with fictitious play. 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, however, many sets of Nash equilibria whose payoffs may be very different from those desired by the social choice function. With monotonic dynamics we show that many equilibria in all the sets of equilibria we describe 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. With fictitious play, if the agents have completely mixed prior beliefs, beliefs and play converge to the outcome the planner wants to implement.

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File URL: https://econ-papers.upf.edu/papers/221.pdf
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Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 221.

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Date of creation: Feb 1997
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Handle: RePEc:upf:upfgen:221
Contact details of provider: Web page: http://www.econ.upf.edu/

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  1. Binmore, K. & Samuelson, L., 1997. "Evolutionary Drift and Equilibrium Selection," Working papers 9729r, Wisconsin Madison - Social Systems.
  2. Dekel, Eddie & Fudenberg, Drew, 1990. "Rational behavior with payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 52(2), pages 243-267, December.
  3. Cabrales, Antonio, 1999. "Adaptive Dynamics and the Implementation Problem with Complete Information," Journal of Economic Theory, Elsevier, vol. 86(2), pages 159-184, June.
  4. Chen, Hsiao-Chi & Friedman, James W. & Thisse, Jacques-Francois, 1997. "Boundedly Rational Nash Equilibrium: A Probabilistic Choice Approach," Games and Economic Behavior, Elsevier, vol. 18(1), pages 32-54, January.
  5. Drew Fudenberg & David Kreps, 2010. "Learning Mixed Equilibria," Levine's Working Paper Archive 415, David K. Levine.
  6. Ponti, Giovanni, 2000. "Cycles of Learning in the Centipede Game," Games and Economic Behavior, Elsevier, vol. 30(1), pages 115-141, January.
  7. I. Gilboa & A. Matsui, 2010. "Social Stability and Equilibrium," Levine's Working Paper Archive 534, David K. Levine.
  8. Sjostrom Tomas, 1994. "Implementation in Undominated Nash Equilibria without Integer Games," Games and Economic Behavior, Elsevier, vol. 6(3), pages 502-511, May.
  9. R. Cressman, K.H. Schlag, 1995. "The Dynamic (In)Stability of Backwards Induction," Discussion Paper Serie B 347, University of Bonn, Germany.
  10. T. Borgers & R. Sarin, 2010. "Learning Through Reinforcement and Replicator Dynamics," Levine's Working Paper Archive 380, David K. Levine.
  11. Karl H. Schlag, 1995. "Why Imitate, and if so, How? A Bounded Rational Approach to Multi-Armed Bandits," Discussion Paper Serie B 361, University of Bonn, Germany, revised Mar 1996.
  12. de Trenqualye, Pierre, 1989. "Stable implementation of Lindahl allocations," Economics Letters, Elsevier, vol. 29(4), pages 291-294.
  13. T. Börgers, 2010. "Weak Dominance and Approximate Common Knowledge," Levine's Working Paper Archive 378, David K. Levine.
  14. Jackson Matthew O. & Palfrey Thomas R. & Srivastava Sanjay, 1994. "Undominated Nash Implementation in Bounded Mechanisms," Games and Economic Behavior, Elsevier, vol. 6(3), pages 474-501, May.
  15. 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.
  16. 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.
  17. Barry Sopher & Dilip Mookherjee, 2000. "Learning and Decision Costs in Experimental Constant Sum Games," Departmental Working Papers 199625, Rutgers University, Department of Economics.
  18. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
  19. 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.
  20. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, March.
  21. 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).
  22. 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.
  23. Hofbauer, Josef & Weibull, Jörgen W., 1995. "Evolutionary Selection against Dominated Strategies," Working Paper Series 433, Research Institute of Industrial Economics.
  24. Binmore, K. & Samuelson, L. & Gale, J., 1993. "Learning to be Imperfect: The Ultimatum Game," Working papers 9325, Wisconsin Madison - Social Systems.
  25. 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.
  26. K. Schlag, 2010. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Levine's Working Paper Archive 454, David K. Levine.
  27. 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.
  28. Marx, Leslie M. & Swinkels, Jeroen M., 1997. "Order Independence for Iterated Weak Dominance," Games and Economic Behavior, Elsevier, vol. 18(2), pages 219-245, February.
  29. repec:cdl:ucsbec:16-97 is not listed on IDEAS
  30. 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.
  31. 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.
  32. Walker, Mark, 1981. "A Simple Incentive Compatible Scheme for Attaining Lindahl Allocations," Econometrica, Econometric Society, vol. 49(1), pages 65-71, January.
  33. 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.
  34. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
  35. 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.
  36. 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.
  37. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
  38. De Trenqualye, Pierre, 1988. "Stability of the Groves and Ledyard mechanism," Journal of Economic Theory, Elsevier, vol. 46(1), pages 164-171, October.
  39. Walker, Mark, 1984. "A simple auctioneerless mechanism with Walrasian properties," Journal of Economic Theory, Elsevier, vol. 32(1), pages 111-127, February.
  40. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
  41. Jordan, J. S., 1986. "Instability in the implementation of Walrasian allocations," Journal of Economic Theory, Elsevier, vol. 39(2), pages 301-328, August.
  42. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October.
  43. 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.
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