Watch populations evolve via replicator dynamics and spatial strategy competition
No one chooses a strategy here. Winning strategies reproduce, losing ones die out, and the population finds its own balance.
Pick a game and drag the initial fraction slider, then watch each strategy's share of the population evolve. Compare Hawk-Dove, the Prisoner's Dilemma, and Coordination.
Hawks fight for resources; Doves share. The ESS is a mix.
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.
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.
Press Play and watch cooperators and defectors play their neighbors on a grid. Notice the clusters of cooperators that hold out.
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.
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