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Local contraction-stability and uniqueness

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  • Andreas M. Hefti

Abstract

This paper investigates the relationship between uniqueness of Nash equilibria and local stability with respect to the best-response dynamics in the cases of sum-aggregative and symmetric games. If strategies are equilibrium complements, local stability and uniqueness are the same formal properties of the game. With equilibrium substitutes, local stability is stronger than uniqueness. If players adjust sequentially rather than simultaneously, this tends towards making a symmetric equilibria of symmetric games more stable. Finally, the relationship between the stability of the Nash best-response dynamics is compared to the stability of the response-dynamics induced by aggregate-taking behavior.

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Bibliographic Info

Paper provided by Department of Economics - University of Zurich in its series ECON - Working Papers with number 112.

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Date of creation: Feb 2013
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Handle: RePEc:zur:econwp:112

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Related research

Keywords: Contraction mapping; stability; uniqueness; aggregate-taking behavior; dominance solvability; symmetric games;

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  1. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February.
  2. Okuguchi, Koji & Yamazaki, Takeshi, 2008. "Global stability of unique Nash equilibrium in Cournot oligopoly and rent-seeking game," Journal of Economic Dynamics and Control, Elsevier, vol. 32(4), pages 1204-1211, April.
  3. Diewert, W. E. & Avriel, M. & Zang, I., 1981. "Nine kinds of quasiconcavity and concavity," Journal of Economic Theory, Elsevier, vol. 25(3), pages 397-420, December.
  4. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer, vol. 26(3), pages 497-516, October.
  5. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
  6. Andreas Hefti, 2011. "On uniqueness and stability of symmetric equilibria in differentiable symmetric games," ECON - Working Papers 018, Department of Economics - University of Zurich.
  7. Dixit, Avinash K, 1986. "Comparative Statics for Oligopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 107-22, February.
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