Evolutionary game theory

Evolutionary game theory studies frequency-dependent selection: the success of a strategy depends on which strategies it encounters.

Payoff matrix

For strategy-frequency vector \(x\) and payoff matrix \(A\), the expected payoff to strategy \(i\) is

while the population mean payoff is

Evolutionary interpretation

Payoff is interpreted as a contribution to fitness or reproductive success. Strategies performing better than the population average can increase in frequency.

Evolutionarily stable strategies

An evolutionarily stable strategy is resistant, under specified conditions, to invasion by a sufficiently rare alternative strategy.