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Evolution, dynamics, and fixed points

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Author Info
Joosten ,Reinoud (MERIT)
Abstract

Sign-compatible dynamics describe changes in the composition of a population driven by differences in fitness. A saturated equilibrium is a fixed point for sign-compatible dynamics where each subgroup with positive population share has highest fitness. An evolutionary stable equilibrium is a saturated equilibrium attracting all trajectories nearby, such that the Euclidean distance to it decreases monotonically. We address existence, multiplicity, and dynamical stability of fixed points of sign-compatible dynamics. A saturated equilibrium may be approximated by using a variable dimension restart algorithm for solving the nonlinear complementarity problem. Journal of Economic Literature Classification Numbers: C62, C68, C72, C73. Keywords: Sign-compatible population dynamics, saturated equilibrium, evolutionary stable equilibrium, dynamic stability, nonlinear complementarity problem.

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Paper provided by Maastricht : MERIT, Maastricht Economic Research Institute on Innovation and Technology in its series Research Memoranda with number 005.

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Date of creation: 1995
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Handle: RePEc:dgr:umamer:1995005

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Keywords: mathematical economics and econometrics;

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  16. Metcalfe, J S, 1994. "Competition, Fisher's Principle and Increasing Returns in the Selection Process," Journal of Evolutionary Economics, Springer, vol. 4(4), pages 327-46, November.
  17. Mailath, George J., 1992. "Introduction: Symposium on evolutionary game theory," Journal of Economic Theory, Elsevier, vol. 57(2), pages 259-277, August. [Downloadable!] (restricted)
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  19. Itzhak Gilboa & Akihiko Matsui, 1990. "A Model of Random Matching," Discussion Papers 887, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  20. Dierker, Egbert, 1972. "Two Remarks on the Number of Equilibria of an Economy," Econometrica, Econometric Society, vol. 40(5), pages 951-53, September. [Downloadable!] (restricted)
  21. Herbert E. Scarf, 1959. "Some Examples of Global Instability of the Competitive Equilibrium," Cowles Foundation Discussion Papers 79, Cowles Foundation, Yale University. [Downloadable!]
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