Too Big to Monitor? Network Scale and the Breakdown of Decentralized Monitoring

Many public services are produced in networked systems where quality depends on local effort and on how higher-level authorities monitor providers. We develop a simple model in which monitoring is a public good on a network with strategic complementarities. A regulator chooses between decentralized monitoring (cheaper, local oversight) and centralized monitoring (more costly, but internalizing spillovers). The model delivers an endogenous centralization threshold: for a given spillover strength, there exists a network size $n^\ast(\lambda)$ above which centralized monitoring strictly dominates; equivalently, for a given network size $n$, there is a critical complementarity $\lambda^\ast(n)$ beyond which decentralized oversight becomes fragile. A stochastic extension suggests that, above this region, idiosyncratic shocks are amplified, producing stronger peer correlations, higher variance, and more frequent deterioration in quality. We test these predictions in the U.S. nursing home sector, where facilities belong to overlapping organizational (chain) and geographic (county) networks. Using CMS facility data, We document strong within-chain and within-county peer effects and estimate network-size thresholds for severe regulatory failure (Special Focus Facility designations). We find sharp breakpoints at roughly 7 homes per county and 34 homes per chain, above which spillovers intensify and deficiency outcomes become more dispersed and prone to deterioration, especially in large counties.