Replicator dynamics
A rule under which the ways of behaving that do better than the population average become more common over time.
Often misread asReading the dynamic as a procedure for finding Nash equilibria, so the trajectory is treated as a search that converges on the answer.
How to see it
Whatever beats the average gets more common
Replicator dynamics describes how the mix of strategies in a population changes over time. A strategy's share grows exactly when its payoff is above the population average and shrinks when it is below. Nobody in the model chooses anything; the proportions move because what does well gets copied or inherited more often.
The checkEvery Nash equilibrium is a rest point, but rest points also include corners where strategies are simply extinct, and some rest points are unstable or orbited rather than approached.
Try itRun the dynamic on rock-paper-scissors. The equal mix is a rest point, yet a population starting slightly off it cycles round forever instead of settling. Ask whether you would still describe that as the dynamic finding the equilibrium.
Games that show it
Know these first
Leads on to
Easily confused with
Sources
- Taylor, P. & Jonker, L. (1978). Mathematical Biosciences 40(1-2), 145-156.
- Weibull, J. (1995). MIT Press.