View More View Less
  • 1 Please ask the editor of the journal.
Restricted access

Nash™s three proofs for the existence of equilibria in strategic games correspond to three dynamics: The best re- sponse dynamics (equivalent to Brown™s fictitious play), the smoothed best response dynamics, and the Brown&von Neumann&Nash dynamics. We prove that an equilibrium which is evolutionarily stable as defined by Maynard Smith is (globally) asymptotically stable for each of these three dynamics.

  • Berger, U. and Hofbauer, J. (1998): The Nash Dynamics. Preprint.

  • Brown, G. W. (1949): Some notes on computation of games solutions. RAND Report P-78.

  • Brown, G. W. (1951): Iterative solution of games by fictitious play. In Activity Analysis of Production and Allocation. Wiley, New York, pp. 374-376.

    Activity Analysis of Production and Allocation , () 374 -376.

  • Weibull, J. W. (1995): Evolutionary Game Theory. MIT Press.

    Evolutionary Game Theory , ().

  • Weibull, J. W. (1994): The Mass-action Interpretation of Nash Equilibrium. Preprint, Stockholm. Revised 1995. Partly published in J. Econ. Theory69 (1996).

    'The Mass-action Interpretation of Nash Equilibrium. Preprint, Stockholm. Revised 1995 ' () 69 J. Econ. Theory .

    • Search Google Scholar
  • Owen, G. (1982): Game Theory. 2nd ed. Academic Press, Orlando.

    Game Theory , ().

  • Swinkels, J. M. (1993): Adjustment dynamics and rational play in games. Games Econom. Behav.5: 455-484.

    'Adjustment dynamics and rational play in games ' () 5 Games Econom. Behav. : 455 -484.

  • Nash, J. (1951): Non-cooperative games. Ann. Math.54: 287-295.

    'Non-cooperative games ' () 54 Ann. Math. : 287 -295.

  • [NASH, J.] The Work of John Nash in Game Theory. Nobel Seminar Dec 8, 1994. J. Econ. Theory69 (1996):153-185.

    () 69 J. Econ. Theory : 153 -85.

  • Nash, J. (1950a): Equilibrium points in N-person games. Proc. Natl. Ac. Sci.36: 48-49.

    'Equilibrium points in N-person games ' () 36 Proc. Natl. Ac. Sci. : 48 -49.

  • Leonard, R. J. (1994): Reading Cournot, reading Nash: The creation and stabilisation of the Nash equilibrium. The Economic Journal104: 492-511.

    'Reading Cournot, reading Nash: The creation and stabilisation of the Nash equilibrium ' () 104 The Economic Journal : 492 -511.

    • Search Google Scholar
  • Maynard Smith, J. (1982): Evolution and the Theory of Games. Cambridge University Press.

    Evolution and the Theory of Games , ().

  • Nash, J. (1950b): Non-cooperative Games. Dissertation, Princeton University, Dept. Mathematics.

  • Maynard Smith, J. and Price, G. (1973): The logic of animal conflicts. Nature246: 15-18.

    'The logic of animal conflicts ' () 246 Nature : 15 -18.

  • Kakutani, S. (1941): A generalization of Brouwer's fixed point theorem. Duke J. Math.8: 457-459.

    'A generalization of Brouwer's fixed point theorem ' () 8 Duke J. Math. : 457 -459.

  • Cressman, R. (1997): Local stability of smooth selection dynamics for normal form games. Math. Social Sciences34: 1-19.

    'Local stability of smooth selection dynamics for normal form games ' () 34 Math. Social Sciences : 1 -19.

    • Search Google Scholar
  • Fudenberg, D. and Levine, D. K. (1998): The Theory of Learning in Games. MIT Press.

    The Theory of Learning in Games , ().

  • Gilboa, I. and Matsui, A. (1991): Social stability and equilibrium. Econometrica59: 859-867.

    'Social stability and equilibrium ' () 59 Econometrica : 859 -867.

  • Brown, G. W. and von Neumann, J. (1950): Solutions of games by differential equations. Ann. Math. Studies24: 73-79.

    'Solutions of games by differential equations ' () 24 Ann. Math. Studies : 73 -79.

  • Hofbauer, J. and Sigmund, K. (1998): Evolutionary Games and Population Dynamics. Cambridge University Press.

    Evolutionary Games and Population Dynamics , ().

  • Hopkins, E. (1999): A note on best response dynamics. Games Econ. Behav.29: 138-150.

    'A note on best response dynamics ' () 29 Games Econ. Behav. : 138 -150.

  • Hofbauer, J. (1995): Stability for the Best Response Dynamics. Preprint.

Selection
Language English
Year of
Foundation
2001
Publication
Programme
ceased
Publisher Akadémiai Kiadó
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 1585-1931 (Print)
ISSN 1588-287X (Online)