Eco-Evolutionary game dynamics with Three Strategies: how geometric analysis provides insights into stability

In this paper we extend a modeling framework that embeds ecological realism by examining how demographic factors determine payoffs, which are subsequently incorporated into evolutionary game models. In particular, it segregates births and deaths, as well as activities in addition to the between player interactions central to the classical theory. In the standard examples of evolutionary games so far considered such as the Hawk-Dove game, a two strategy population has been studied. The above demographic models are extended from two strategies to three strategies, giving a thorough analysis of the mechanistic framework, which lays down the necessary conditions on the existence of steady states for a constrained system. We show that population trajectories are drawn toward the density manifold by logistic suppression, which in turn structures the interaction between frequency dynamics and fixed points. We also introduce a novel approach which helps derive stability from geometric insights through phase space elements (nullclines and their intersections) and streamlines calculations by decomposing gradients into the components that contribute to directional change, allowing dynamic and stability conditions to be more easily interpreted directly from the figures.