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Evolution, dynamics, and fixed points

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  • 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.

Suggested Citation

  • Joosten, Reinoud, 1995. "Evolution, dynamics, and fixed points," Research Memorandum 005, Maastricht University, Maastricht Economic Research Institute on Innovation and Technology (MERIT).
  • Handle: RePEc:unm:umamer:1995005
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    References listed on IDEAS

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    More about this item

    Keywords

    mathematical economics and econometrics;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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