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.
Activity Analysis of Production and Allocation374376)| false