The simplex of 3-strategy evolutionary games. Trajectories flow toward Nash equilibria or limit cycles. Includes Rock-Paper-Scissors, Hawk-Dove, Prisoner's Dilemma, and Stag Hunt.
Classic game
Payoff matrix A (row=player, col=opponent)
Strategies: S₁, S₂, S₃
Number of trajectories12
Time horizon T20
Replicator equation: ẋᵢ = xᵢ[(Ax)ᵢ − x·Ax]
Strategies grow when their fitness (Ax)ᵢ exceeds mean fitness x·Ax. The simplex Δ₃ = {x: x₁+x₂+x₃=1, xᵢ≥0} is invariant. RPS: Interior fixed point is a center (Zeeman, 1980) — trajectories spiral or cycle. ESS: A strategy p* is an ESS if it cannot be invaded by any mutant. ESS ↔ asymptotically stable fixed point of replicator dynamics. Nash equilibria are fixed points; not all are stable. Click the simplex to launch a trajectory from that point.