Suppose a group of two individuals. Individuals' interactions follow an additive prisoner's dilemma:

\begin{array}{c c c} & C & D \\ \text{Cooperate (} C \text{)} & b -c & -c \\ \text{Defect (} D\text{)} & b & 0 \end{array} where $b$ is the benefit and $c$ is the cost. The payoffs are to the player on the left. I need to calculate the regression of individual fitness on individual phenotype, $\beta (w_i, p_i)$, where $p_i = 0$ if $i$ defects and $p_i = 1$ if $i$ cooperates.

I thought that the right way of calculating $\beta(w_i,p_i)$ would be to vary the strategy of the focal individual while keeping the strategy of the other individual constant (my impression was that the other individual becomes the environment for the focal individual). Because switching to cooperation causes an individual to lose $-c$ in fitness (if we keep the strategy of the other individual constant), I thought that $\beta(w_i,p_i) = -c$. But, to my surprise, $\beta(w_i,p_i) = -b -c$.

Let $V(X|Y)$ be the payoff of individual $X$ when it interacts with $Y$ ($X$ is the focal individual; $Y$ is the other individual). I understand that to get the right answer I have to subtract $V(C|D) - V(D|C)$ --- as opposed to $V(C|C) - V(D|C)$. My question is why this is the right way of calculating $\beta(w_i,p_i)$.