Cooperative Mechanism Games for Oversight of Agent Populations under Partitioned Observation

A deployed population of AI agents seldom has a single overseer. A model provider observes inference traffic; a platform operator observes tool calls; a sectoral regulator observes downstream outcomes. Each can adjust only its own instrument, each sees only its own slice of agent behaviour, yet the harm they all care about depends on the full action profile. We formalise this as a Cooperative Mechanism Game (CMG): $K$ principals sharing one objective, with constrained instruments and observation kernels that project the agent action profile onto principal-specific signals. We define a governance gap comparing welfare under pooled and partitioned observation, split it into an information-partitioning term and a coordination term, then show that the four resulting benchmarks form a lattice whose total gap is path invariant. In a quadratic-Gaussian instance with $K$ overseers of a shared resource we obtain the information-partitioning gap in closed form. It is linear in shock variance, increasing and bounded in the strength of the externality, positive even when instruments are free, because convex private effort makes asymmetric instruments wasteful. Noise in each overseer's view of the state scales the gap by the share of state variance the signal explains and never closes it; noise in the view of agent behaviour, with no state to track, leaves it at zero. The coordination term is zero in this instance for any instrument prices, while two variants with substitutable instruments or discrete targeting produce equilibrium multiplicity and a positive coordination gap. The framework gives a quantitative handle on whether distributing oversight over a population of agents is harmless or expensive. It also identifies which failure mode to repair first.