Constructing Patterns of (Many) ESSs Under Support Size Control

Immanuel M. Bomze () and Werner Schachinger
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Immanuel M. Bomze: University of Vienna
Werner Schachinger: University of Vienna

Dynamic Games and Applications, 2020, vol. 10, issue 3, No 3, 618-640

Abstract: 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.

Keywords: Local solutions; Quadratic optimization; Evolutionary stability; Global optimization (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13235-019-00323-1

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