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Evolutionary stability and Nash equilibrium in finite populations, with an application to price competition

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  • Ania, Ana B.

Abstract

Schaffer [Schaffer, M.E., 1988. Evolutionarily stable strategies for a finite population and a variable contest size. Journal of Theoretical Biololgy 132, 469-478] proposed a concept of evolutionary stability for finite-population models that has interesting implications in economic models of evolutionary learning, since it is related to perfectly competitive equilibrium. The present paper explores the relation of this concept to Nash equilibrium in particular classes of games, including constant-sum games, games with weak payoff externalities, and games where imitative decision rules are individually improving. An illustration of the latter is provided in the context of Bertrand oligopoly with homogeneous product which allows for a characterization of the set of evolutionarily stable prices.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Behavior & Organization.

Volume (Year): 65 (2008)
Issue (Month): 3-4 (March)
Pages: 472-488

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Handle: RePEc:eee:jeborg:v:65:y:2008:i:3-4:p:472-488

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  1. Yasuhito Tanaka, 1999. "Long run equilibria in an asymmetric oligopoly," Economic Theory, Springer, vol. 14(3), pages 705-715.
  2. Schlag, Karl H., 1994. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Discussion Paper Serie B 296, University of Bonn, Germany.
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Citations

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Cited by:
  1. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2010. "Unbeatable Imitation," Working Papers 0499, University of Heidelberg, Department of Economics.
  2. Thomas Vallée & Murat Yıldızoğlu, 2013. "Can They Beat the Cournot Equilibrium? Learning with Memory and Convergence to Equilibria in a Cournot Oligopoly," Computational Economics, Society for Computational Economics, vol. 41(4), pages 493-516, April.
  3. Tobias Guse & Burkhard Hehenkamp & Alex Possajennikov, 2008. "On the Equivalence of Nash and Evolutionary Equilibrium in Finite Populations," Discussion Papers 2008-06, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
  4. Ana B. Ania & Andreas Wagener, 2009. "The Open Method of Coordination (OMC) as an Evolutionary Learning Process," CESifo Working Paper Series 2601, CESifo Group Munich.
  5. Peter Duersch & Joerg Oechssler & Burkhard Schipper, 2010. "Pure Strategy Equilibria in Symmetric Two-Player Zero-Sum Games," Working Papers 1021, University of California, Davis, Department of Economics.
  6. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2010. "Pure Saddle Points and Symmetric Relative Payoff Games," Working Papers 0500, University of Heidelberg, Department of Economics.
  7. Manfred Nermuth, 2008. "The Structure of Equilibrium in an Asset Market with Variable Supply," Vienna Economics Papers 0804, University of Vienna, Department of Economics.
  8. Matsumura, Toshihiro, 2012. "Welfare consequence of an asymmetric regulation in a mixed Bertrand duopoly," Economics Letters, Elsevier, vol. 115(1), pages 94-96.

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