Frequency-dependent payoff ($f_i(x)$)

A frequency-dependent payoff is an expected payoff depending on the population composition $x$. Under random pairwise encounters with a fixed payoff matrix it is the linear function $f_i(x)=(Ax{)}_i$. The relative advantage $f_i(x)-f_j(x)$ can change sign as opponents become more or less common. The replicator equation converts this feedback into changes of frequency; nonlinear frequency-dependent payoffs allow interactions not represented by a fixed pairwise table.