Monotone path-summed estimator for locally observable games

In a locally observable finite partial-monitoring game, choose a Pareto-cell cover $S$. There is a finite constant $V\ge0$ such that, for every mixed outcome $\lambda$, local estimators can be summed along the loss-monotone neighbour paths to form a vector estimator $f$. It is uniformly bounded by $V$, and whenever $f(a,\sigma)_b\ne0$, action $a$ has no larger $\lambda$-expected loss than comparator $b$.\n\nThe estimator telescopes along each path to estimate $L_b-L_{\mathrm{root}}$. Lemma 37.8 shows that every revealing action in an edge neighbourhood has loss between the two endpoint losses, which gives the monotone-support property.\n\nFormalization Note A crude finite sum of all selected edge-estimator norms supplies $V$; only existence of a game-dependent constant is needed downstream.