This raises the issue of determining how $A$ chooses $D_A$ given that $B$ is choosing $D_B$. Given a function $s_{-G}=(s_A,s_B)$, $B$'s contract $D_B$ and G's decision $S_G$, $A$ chooses a contract in order to maximize his payoff. \begin{align}\label{AsNprob}
\max_{D_A} &\quad  s_A(D_{S_G(\mathcal{D}_G)})^T U_A^{D_A}s_B(D_{S_G(\mathcal{D}_G)})
\end{align}
