Abstract
In this article, we focus on studying the passivity properties of different versions of replicator dynamics (RD). The RD represents a deterministic monotone nonlinear dynamic, which allows incorporation of the distribution of population types through a fitness function. We use tools for control theory, in particular, the passivity theory, to study the stability of the RD when it is in action with evolutionary games. The passivity theory allows us to identify the class of evolutionary games in which stability with RD is guaranteed. We show that several variations of the first order RD satisfy the standard loseless passivity property. In contrary, the second-order RD does not satisfy the standard passivity property; however, it satisfies a similar dissipativity property known as negative imaginary property.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
