= Tit for tat invasion of a reactive resident
{c}
{title2=$w_T-w_M=\epsilon[R-g(z)]$}
For a reactive resident $(p,q)$ with $|p-q|<1$, let $z=q/(1-p+q)$ and $g(z)=Rz^2+(S+T)z(1-z)+P(1-z)^2$. Its self-payoff and both ordered cross-payoffs against <Tit for tat> equal $g(z)$. At introduced <Tit for tat> frequency $\epsilon$, its fitness difference is therefore the displayed expression. If $2R\ge S+T$, it is positive for $z<1$ because $R-g(z)=(1-z)[R-P+(R+P-S-T)z]$. Fully cooperative reached histories tie; the deterministic opposite-response strategy needs a separate cycle calculation. Initial advantage is order frequency rather than a positive invasion exponent at zero.
Back to article page
