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Large Deviations and Equilibrium Selection in Large Populations

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  • Alan Beggs

Abstract

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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Bibliographic Info

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

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Keywords: equilibrum selection; large deviations; large populations; games;

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  1. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
  2. D. Foster & P. Young, 2010. "Stochastic Evolutionary Game Dynamics," Levine's Working Paper Archive 493, David K. Levine.
  3. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  4. Diamond, Peter A, 1982. "Aggregate Demand Management in Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 90(5), pages 881-94, October.
  5. D. Fudenberg & C. Harris, 2010. "Evolutionary Dynamics with Aggregate Shocks," Levine's Working Paper Archive 496, 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. Alan Beggs, 2003. "Waiting Times and Equilibrium Selection," Economics Series Working Papers 142, University of Oxford, Department of Economics.
  8. K. Binmore & L. Samuelson & K. Vaughn, 2010. "Musical Chairs: Modelling Noisy Evolution," Levine's Working Paper Archive 487, David K. Levine.
  9. J Bergin & B L Lipman, 1997. "Evolution with state-dependent Mutations," Levine's Working Paper Archive 771, 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. F. Biesmans, 1977. "A Survey," Annals of Public and Cooperative Economics, Wiley Blackwell, vol. 48(1), pages 5-36, 01.
  12. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
  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. Alan Beggs, 2002. "Stochastic evolution with slow learning," Economic Theory, Springer, vol. 19(2), pages 379-405.
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