Assumptions

$(c.5)$

For all $\underline{\gamma}\in\Gamma$ s.t. $J(\underline{\gamma})<\infty$, the following RVs are integrable: $$\nabla_{u^{i}}L(\xi;\underline{\gamma}^{*}(\mathbf{y}))[\gamma^{i}(y^{i})-\gamma^{i*}(y^{i})],\quad i\in\mathcal{N}$$ ## $(c.6)$ $\Gamma^{i}$ is a Hilbert Space for each $i\in\mathcal{N}$, and $J(\underline{\gamma})<\infty$ for all $\underline{\gamma}\in\Gamma$. Furthermore, $$E_{\xi|y^{i}}\left[ \nabla_{u^{i}}L(\xi;\underline{\gamma}^{*}(\mathbf{y})) \right]\in\Gamma^{i}\quad i\in\mathcal{N}$$ # Theorem Let $\{ J;\Gamma^{i},i\in\mathcal{N} \}$ be a static stochastic team problem which satisfies all of the hypotheses of Theorem 2.4.5, with the exception of (⭐). Instead let either $(c.5)$ or $(c.6)$ hold. Then, if $\underline{\gamma}^{*}\in\mathbf{\Gamma}$ is a stationary policy it is also team-optimal. Such a policy is unique if $L(\xi;\mathbf{u})$ is strictly convex in $\mathbf{u}$, a.s..