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Evolutionary Dynamics and Equilibria

Weakly compatible population dynamics describe changes in the composition of a population in a competitive environment, driven by differences in fitness levels within the population. We introduce the saturated equilibrium and the evolutionary stable equilibrium as (dynamic) generalizations of the Nash-equilibrium and the evolutionary stable strategy of evolutionary games. We examine the dynamic properties of these equilibrium concepts and relate them to equilibrium concepts from noncooperative game theory. The issues of existence, multiplicity, dynamical stability, and computability of equilibria are addressed. A variable dimension restart algorithm to solve the nonlinear complementarity problem may be used to compute a saturated equilibrium.