Replicator Equation — Evolutionary Game Dynamics

Simplex flow ẋᵢ = xᵢ[(Ax)ᵢ − x·Ax] on the strategy simplex

The replicator equation governs strategy frequency evolution under natural selection: strategies with above-average fitness grow. Rock-paper-scissors produces cycling orbits; Hawk-Dove has a mixed ESS; Coordination has two pure Nash equilibria as attractors on the simplex boundary.