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Constructing Patterns of (Many) ESSs Under Support Size Control

Author

Listed:
  • Immanuel M. Bomze

    (University of Vienna)

  • Werner Schachinger

    (University of Vienna)

Abstract

As is well known, equilibrium analysis of evolutionary partnership games can be done by studying a so-called standard quadratic optimization problem, where a possibly indefinite quadratic form is maximized over the standard (probability) simplex. Despite the mathematical simplicity of this model, the nonconvex instances in this problem class allow for remarkably rich patterns of coexisting (strict) local solutions, which correspond to evolutionarily stable states (ESSs) in the game; seen from a dynamic perspective, ESSs form the asymptotically stable fixed points under the continuous-time replicator dynamics. In this study, we develop perturbation methods to enrich existing ESS patterns by a new technique, continuing the research strategy started by Chris Cannings and coworkers in the last quarter of the past century.

Suggested Citation

  • Immanuel M. Bomze & Werner Schachinger, 2020. "Constructing Patterns of (Many) ESSs Under Support Size Control," Dynamic Games and Applications, Springer, vol. 10(3), pages 618-640, September.
    • Handle: RePEc:spr:dyngam:v:10:y:2020:i:3:d:10.1007_s13235-019-00323-1
    DOI: 10.1007/s13235-019-00323-1
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    References listed on IDEAS

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    1. Immanuel M. Bomze & Werner Schachinger & Reinhard Ullrich, 2018. "The Complexity of Simple Models—A Study of Worst and Typical Hard Cases for the Standard Quadratic Optimization Problem," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 651-674, May.
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    Cited by:

    1. D. Timothy Bishop & Mark Broom & Richard Southwell, 2020. "Chris Cannings: A Life in Games," Dynamic Games and Applications, Springer, vol. 10(3), pages 591-617, September.

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