Chapter 4 connects the dynamic steady state concepts analyzed in previous chapters to the classic static concepts of Nash equilibrium (NE) and evolutionarily stable state (ESS). It shows that NE is a necessary condition for a steady state to be dynamically stable, and that ESS is sufficient under replicator dynamics, but is not always sufficient for other monotone dynamics. It applies equilibrium ideas to established models of Fisherian runaway sexual selection, and also introduces the concept of an adjustment matrix, which modifies the payoff matrix via the Hadamard product (element-by-element matrix multiplication). A technical appendix explains three main techniques of stability analysis: eigenvalues of (projected) Jacobian matrices, Lyapunov functions, and Liouville’s theorem.
Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
If you think you should have access to this title, please contact your librarian.