Irreducible Governance Structure for Autonomous Agent Systems: Fair Allocation, Strategy-Proofness, and Multi-Scale Composition

Autonomous agent governance is commonly framed as a problem of enforcing correct execution. However, in multi-agent systems, an equally fundamental question precedes execution:which agents are allowed to act.In this paper, we show that allocation is not an auxiliary concern but a structural component of governance. When multiple agents compete for execution under constrained resources,any allocation mechanism introduces unavoidable trade-offs between fairness, efficiency, andresistance to strategic manipulation. We formalize this through a set of impossibility results,including Sybil amplification and the incompatibility of desirable allocation properties.We then show that these allocation constraints cannot be resolved within a single layer ofcontrol. Instead, they propagate across the system, interacting with execution atomicity, stateenforcement, and behavioral drift. This leads to a multi-scale governance structure composedof four orthogonal dimensions: temporal (atomicity), state (enforcement), behavioral (driftmonitoring), and population (allocation).Our main result is an irreducibility theorem: under finite observability, no governance architecture can collapse these dimensions without loss of correctness or stability. Allocation, inparticular, acts as a first-class constraint that prevents simplification of the governance stack.Wevalidate these results through a series of analytical constructions and empirical ablations,showing that removing or approximating any layer leads to systematic failure modes.1This work reframes agent governanceas a structural problem: not only how actions areexecuted, but how access to executionis determined, and why these decisions impose irreduciblearchitectural requirements.