A Formal Analysis of Agent Payment Protocols

Agent payment protocols are emerging as a key transaction layer for autonomous commerce, enabling AI agents to purchase goods and services and execute payments on users' behalf. Unlike conventional payment flows, they distribute user intent, delegated authority, credential use, settlement, and fulfillment across multiple actors and stages, creating security dependencies that no single message or participant can enforce. Yet these guarantees remain largely implicit across evolving specifications, schemas, and reference implementations, with little systematic formal analysis. We formalize four representative agent payment protocols: x402, MPP, ACP, and AP2 in Tamarin. Using a common abstraction of the agent payment lifecycle, we construct source-grounded models that capture each protocol's roles, state, trust assumptions, and lifecycle transitions. Rather than assuming a complete property taxonomy, we use source-backed verification questions and counterexample traces to expose missing bindings, state constraints, and cross-stage correspondences, consolidating them into 18 shared security principles. Across 86 verification cases, our analysis reproduces 46 known or calibration cases and identifies 40 previously undocumented formal-consistency findings. For each retained violation, we isolate the missing protocol relation, construct a minimally strengthened reference model, and reverify the intended property. We further evaluate the new x402 findings across three implementations and validate ten representative findings through implementation PoCs, SDK/schema-level witnesses, and source-aligned executable traces spanning five security principles. Our results show that delegated authorization must remain consistent with its resulting economic and service effects across actors, states, and protocol stages.