Evolutionary Game Theory
Studies strategy frequencies in large populations under selection and mutation.
Definition
Strategies are heritable phenotypes; fitness equals expected game payoff against a random opponent from the current population state .
Solution concepts include evolutionarily stable strategies (ESS) and asymptotically stable rest points of evolutionary dynamics.
Intuition
No foresight or rationality is required — selection substitutes for best-response reasoning.
Equilibrium emerges from differential reproduction of successful strategies.
Worked example
The Hawk-Dove game admits a mixed ESS at for value and cost .
Sex-ratio evolution gives a ratio as an ESS (Fisher).
The math
Every ESS is a Nash equilibrium of the symmetric game; the converse requires additional stability conditions.
Replicator dynamics link EGT to Lyapunov analysis and relative entropy.
Where it is used
Biology (animal conflicts, signaling), cultural evolution, learning in games, and multi-agent RL.
Explains seemingly irrational persistence of cooperation in animal populations.
More in Game theory
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