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Large Deviations and Equilibrium Selection in Large Populations

  • Alan Beggs

This paper uses the theory of large deviations to analyse equilibrium selection in one-dimensional games with large populations where the system evolves according to a jump Markov process. The equilibria selected maximise a quasi-potential function which can be determined by solving a polynomial equation. Estimates of waiting times are also given. It shows that equilibria about which there is more noise are less likely to be selected and clarifies the role of the limiting deterministic dynamic in selection.

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File URL: http://www.economics.ox.ac.uk/materials/working_papers/paper129.pdf
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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 129.

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Date of creation: 01 Nov 2002
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Handle: RePEc:oxf:wpaper:129
Contact details of provider: Postal: Manor Rd. Building, Oxford, OX1 3UQ
Web page: http://www.economics.ox.ac.uk/
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  1. P. Diamond, 1980. "Aggregate Demand Management in Search Equilibrium," Working papers 268, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
  3. F. Biesmans, 1977. "A Survey," Annals of Public and Cooperative Economics, Wiley Blackwell, vol. 48(1), pages 5-36, 01.
  4. Alan Beggs, 2005. "Waiting times and equilibrium selection," Economic Theory, Springer, vol. 25(3), pages 599-628, 04.
  5. J. Bergin & B. Lipman, 2010. "Evolution with State-Dependent Mutations," Levine's Working Paper Archive 486, David K. Levine.
  6. Benaim, Michel & Weibull, Jörgen W., 2000. "Deterministic Approximation of Stochastic Evolution in Games," Working Paper Series 534, Research Institute of Industrial Economics, revised 30 Oct 2001.
  7. Fudenberg, D. & Kreps, D.M., 1992. "Learning Mixed Equilibria," Working papers 92-13, Massachusetts Institute of Technology (MIT), Department of Economics.
  8. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  9. D. Foster & P. Young, 2010. "Stochastic Evolutionary Game Dynamics," Levine's Working Paper Archive 493, David K. Levine.
  10. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
  11. Alan Beggs, 2000. "Stochastic Evolution with Slow Learning," Economics Series Working Papers 33, University of Oxford, Department of Economics.
  12. Fudenberg, Drew & Harris, Christopher, 1992. "Evolutionary Dynamics with Aggregate Shocks," IDEI Working Papers 13, Institut d'Économie Industrielle (IDEI), Toulouse.
  13. Ellison, Glenn, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," Review of Economic Studies, Wiley Blackwell, vol. 67(1), pages 17-45, January.
  14. K. Binmore & L. Samuelson & K. Vaughn, 2010. "Musical Chairs: Modelling Noisy Evolution," Levine's Working Paper Archive 487, David K. Levine.
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