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Implementation, elimination of weakly dominated strategies and evolutionary dynamics

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  • Antonio Cabrales
  • Giovanni Ponti

Abstract

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: http://www.econ.upf.edu/docs/papers/downloads/221.pdf
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Bibliographic Info

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

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Web page: http://www.econ.upf.edu/

Related research

Keywords: Implementation; bounded rationality; evolutionary dynamics; mechanisms;

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References

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Citations

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Cited by:
  1. Antonio Cabrales & Roberto Serrano, 2007. "Implementation in Adaptive Better-Response Dynamics," Economics Working Papers we075731, Universidad Carlos III, Departamento de Economía.
  2. Cason, Timothy N. & Saijo, Tatsuyoshi & Sjostrom, Tomas & Yamato, Takehiko, 2003. "Secure Implementation Experiments: Do Strategy-proof Mechanisms Really Work?," Working Papers 4-03-1, Pennsylvania State University, Department of Economics.
  3. 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).
  4. Marco Galbiati, 2006. "Fair Divisions as Attracting Nash Equilibria of Simple Games," Economics Working Papers ECO2006/24, European University Institute.
  5. Maskin, Eric & Sjostrom, Tomas, 2001. "Implementation Theory," Working Papers 5-01-1, Pennsylvania State University, Department of Economics.
  6. Sandholm,W.H., 1999. "Evolutionary implementation and congestion pricing," Working papers 38, Wisconsin Madison - Social Systems.
  7. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Economics Working Papers 0033, Institute for Advanced Study, School of Social Science.
  8. Norovsambuu Tumennasan, 2011. "To Err is Human: Implementation in Quantal Response Equilibria," Economics Working Papers 2011-11, School of Economics and Management, University of Aarhus.
  9. David K Levine & Aldo Rustichini, 2000. "Introduction: The Dynamic Games Special Issue," Levine's Working Paper Archive 2127, David K. Levine.
  10. Jordi Brandts & Antonio Cabrales & Gary Charness, 2007. "Forward induction and entry deterrence: an experiment," Economic Theory, Springer, vol. 33(1), pages 183-209, October.
  11. Sandholm,W.H., 2001. "Negative externalities and evolutionary implementation," Working papers 15, Wisconsin Madison - Social Systems.
  12. 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.

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