  A stable steady state of a dynamical system is a state \(s\) with the following two features: once the system enters \(s\), it never leaves it; and once the system approaches “close enough” to \(s\), then it always remains near \(s\). The basin of attraction of \(s\) is the set of states such that, if the dynamical system begins in one of those states, then it will eventually converge towards \(s\). In many cases, the best way to understand a dynamical system is to construct a “phase portrait” diagramming its steady states and their basins of attraction. In the case of interest to us here, the “state” of a dynamical system is simply the proportion of players choosing each strategy.