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Replicator Dynamics

Continuous-time evolutionary game theory. Strategies reproduce proportionally to their fitness. Watch populations evolve, visualize phase portraits, and discover evolutionarily stable strategies (ESS).

Payoff Matrix (Row Strategy)

Strategy A
Strategy B
Strategy A
Strategy B
50%
5

System Analysis

Strategy A % 50.0%
Strategy B % 50.0%
Fitness A -
Fitness B -
Equilibrium -

About Replicator Dynamics

The Model: Replicator dynamics describes how strategy frequencies change over time in evolutionary game theory. Strategies with higher-than-average fitness grow in frequency.

The Equation: dx/dt = x(1-x)[f(A,A)x + f(A,B)(1-x) - f(B,A)x - f(B,B)(1-x)]

Where x is the frequency of Strategy A, and f(X,Y) is the payoff for playing X against Y.

Equilibria Types:

• Stable (Attractor): Nearby trajectories converge to this point (ESS)

• Unstable (Repeller): Nearby trajectories diverge away

• Neutral: Trajectories neither converge nor diverge

Phase Portrait: The visualization shows all possible evolutionary trajectories. Arrows indicate direction of evolution. The horizontal axis represents the frequency of Strategy A (0% to 100%).

Examples:

• Hawk-Dove: Internal ESS at x = V/C (mixed population)

• Prisoner's Dilemma: Defection is the only ESS (cooperation dies out)

• Stag Hunt: Two stable equilibria (bistable system)

• Coordination: Similar to Stag Hunt but with different payoffs

Click "Add Trajectory" to see evolution from different starting points!