Evolutionary Dynamics and Lipschitz Maps
John Cleveland

TL;DR
This paper develops a simplified, Lipschitz-based mathematical framework for analyzing fully nonlinear evolutionary game models, enabling better understanding of well-posedness, asymptotic behavior, and parameter estimation.
Contribution
It introduces a Banach space approach with Lipschitz rates and a new multiplication method, improving the analysis and enabling parameter estimation in evolutionary game models.
Findings
Model is uniformly eventually bounded under biological assumptions.
The framework forms a locally Lipschitz semiflow covering various models.
The approach simplifies the analysis by using a single norm inducing the weak* topology.
Abstract
In \cite{ CLEVACKTHI, CLEVACK} an attempt is made to find a comprehensive mathematical framework in which to investigate the problems of well-posedness, asymptotic analysis and parameter estimation for fully nonlinear evolutionary game models. A theory is developed as a dynamical system on the state space of finite signed Borel measures under the weak star topology. Two drawbacks of the previous theory is that the techniques and machinery involved in establishing the results are awkward and have not shed light on the parameter estimation question. For example, in \cite{CLEVACK} the proof for the existence of the dynamical system is obtained via a fixed point argument using the total variation topology, however, the continuity of the model is established in the topology. This has caused some confusion. I have remedied this by making all the vital rates Lipschitz and the…
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Taxonomy
TopicsEvolution and Genetic Dynamics · Evolutionary Game Theory and Cooperation · Game Theory and Applications
