Theorem 2.4.4

For an $N$-agent static stochastic team problem, let 1. The hypotheses $(c.3)$ and $(c.4)$ be satisfied; 2. $S^{i}$ be an Open convex subset of a finite dimensional Vector Space for each $i\in\mathcal{N}$; 3. $L(\xi;\cdot)$ be convex and continuously differentiable on $\mathbf{S}:=S^{1}\times\dots \times S^{N}$ Under these conditions, if the policy $\underline{\gamma}^{\circ}$, taking values in $\mathbf{S}$, is stationary, it is team-optimal.