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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. Beggs, A., 2000. "Stochastic Evolution with Slow Learning," Economics Series Working Papers 9933, University of Oxford, Department of Economics.
  2. Michel BenaÔm & J–rgen W. Weibull, 2003. "Deterministic Approximation of Stochastic Evolution in Games," Econometrica, Econometric Society, vol. 71(3), pages 873-903, 05.
  3. 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.
  4. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  5. 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.
  6. Alan Beggs, 2003. "Waiting Times and Equilibrium Selection," Economics Series Working Papers 142, University of Oxford, Department of Economics.
  7. BERGIN, James & LIPMAN, Bart, 1994. "Evolution with State-Dependent Mutations," CORE Discussion Papers 1994055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. D. Fudenberg & C. Harris, 2010. "Evolutionary Dynamics with Aggregate Shocks," Levine's Working Paper Archive 496, David K. Levine.
  9. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
  10. Fudenberg, D. & Kreps, D.M., 1992. "Learning Mixed Equilibria," Working papers 92-13, Massachusetts Institute of Technology (MIT), Department of Economics.
  11. K. Binmore & L. Samuelson & K. Vaughn, 2010. "Musical Chairs: Modelling Noisy Evolution," Levine's Working Paper Archive 487, David K. Levine.
  12. D. Foster & P. Young, 2010. "Stochastic Evolutionary Game Dynamics," Levine's Working Paper Archive 493, David K. Levine.
  13. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
  14. F. Biesmans, 1977. "A Survey," Annals of Public and Cooperative Economics, Wiley Blackwell, vol. 48(1), pages 5-36, 01.
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