Table 2.

The categorization of players as free‐riders or contributors. All players within a group can be classed as a contributor or free‐rider depending on their frequency. The frequency threshold that separates the two classes depends on the costs (c) and benefits (b) of investment into public goods. Once classified, players can be assigned an investment level (${\widehat{\mathbf{x}}}_{\mathbf{i}}$) and expected fitness (ω_i)

Investment class	Frequency limit	Investment level	Fitness
Free‐rider	${\displaystyle p_i<\frac{\overline{p}nb+c}{b(n+1)}}$	${\displaystyle {\widehat{x}}_i=0}$	${\displaystyle {\omega }_i=\frac{(\overline{p}nb+c)}{c(n+1)}}$
Contributor	${\displaystyle p_i\ge \frac{\overline{p}nb+c}{b(n+1)}}$	${\displaystyle {\widehat{x}}_i=\frac{p_{i}b-c-n(\overline{p}-p_i)b}{p_{i}bc(n+1)}}$	${\displaystyle {\omega }_i=\frac{{(\overline{p}nb+c)}^2}{p_{i}bc{(n+1)}^2}}$