Watch populations evolve via replicator dynamics and spatial strategy competition
Evolutionary game theory asks: what happens when a population of agents play a game repeatedly, and the more successful strategies reproduce faster? Instead of rational players choosing strategies, natural selection does the choosing.
The replicator equation describes how strategy frequencies change over time: strategies with above-average fitness grow, below-average ones shrink. The fixed points of this equation correspond to evolutionary stable states.
Watch how the fraction of the population playing each strategy evolves over time. Drag the initial condition slider to see how different starting points lead to different outcomes.
Hawks fight for resources; Doves share. The ESS is a mix.
Try this: In the Hawk-Dove game, notice how the population converges to an interior equilibrium — a mix of hawks and doves. In the Prisoner's Dilemma, cooperators always go extinct. In the Coordination game, the outcome depends entirely on the initial condition.
When agents only interact with their neighbors on a grid, spatial structure can sustain cooperation even in the Prisoner's Dilemma. Cooperators form clusters that protect their interior members from exploitation.
Key insight: Spatial structure fundamentally changes the dynamics. In a well-mixed population, defectors always win the Prisoner's Dilemma. On a grid, cooperators can survive by forming protective clusters — the geometry of interaction matters.