Frequency-dependent payoff (source code)

= Frequency-dependent payoff
{title2=$f_i(x)$}

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.