PARTIAL OBSERVABILITY APPROACH FOR THE OPTIMAL TRANSPARENCY PROBLEM IN MULTI-AGENT SYSTEMS

The paper proves existence/uniqueness and convergence for x(t+1)=max(0,(I−W)H_p x(t)+b) by a contraction argument on successive differences using ‖I−W‖<1 and ‖H_p‖=1 (Theorem 1; eqs. (17)–(23)) , characterizes the equilibrium via an LCP (Theorem 2; eqs. (24)–(28)) , gives the closed-form when x*>0 with a Neumann approximation (eqs. (29)–(31)) and a sufficient condition for strict positivity (Theorem 3; eqs. (32)–(33)) . The candidate solution reproduces these results via Banach’s fixed-point theorem (instead of the paper’s Cauchy-difference approach), the same LCP, the same positivity condition (modulo a minor inequality-direction slip), and the same Neumann expansion. The norm choice is consistent with the paper’s notation (∞-norm) and assumptions on S_i and b_i match the setup (Section 3.1) . Aside from the small inequality sign slip when relating ‖(I−W)H_p‖ to ‖I−W‖, the model’s reasoning aligns with the paper.