The Price of Over-Delegation: Stackelberg Liability Design for Agentic AI Handoffs

As LLM-based agents are increasingly deployed in sequential delegation chains, each handoff can obscure accountability for the final output, leading to context loss, audit overhead, and diffusion of responsibility. We formulate this governance problem as a Stackelberg game: a regulator sets a liability share, and developers choose a workflow partition via a boundary-insertion game on a sequential workflow DAG. The induced game is an exact potential game for every liability share $\gamma \in (0,1]$, and under a continuous relaxation admits a unique interior equilibrium. We prove an over-fragmentation theorem: when developers only partially internalize handoff externalities ($\gamma < 1$), the equilibrium delegation depth strictly exceeds the social optimum, and the resulting welfare loss admits a scale-free closed-form expression independent of workflow size, agent productivity, and handoff-cost scale. We characterize the optimal liability share $\gamma^*$ via a first-order condition that balances the marginal welfare gain against the marginal enforcement cost, and derive comparative statics. Under optimal regulation, residual welfare loss scales quadratically with enforcement cost, suggesting that reductions in enforcement costs yield more-than-proportional welfare gains.