Quick answerGive every agent a documented precedence hierarchy it can apply in the moment, not just a long term fix. A common working rule: the agent that owns the domain the question falls under wins by default, timestamp of last policy sync breaks ties within the same domain, and any contradiction involving money, legal terms, or safety always escalates to a human rather than letting either agent unilaterally declare itself correct. The agent should say plainly that it found a conflicting answer elsewhere and that it is checking, rather than either doubling down or silently overriding its sibling.
Why the standard fix is not enough for the live moment
The standard fix for two of your own AI agents giving different answers is a shared source of truth that both agents query at answer time, which is the right long term architecture. But that fix takes real engineering time to design and roll out, and it does nothing for the customer sitting in a conversation right now, who has already been told two different things by two systems from the same company. You need a protocol for the live moment that does not depend on the underlying architecture already being fixed.
The precedence hierarchy an agent can apply without a human in the loop
Give each agent a simple, ordered rule it can evaluate on its own: does this question fall inside my domain of ownership, or my sibling's? A billing question that a sales agent gets asked mid pitch should defer to the support agent's answer if support owns billing policy, even if the sales agent technically generated a plausible sounding response. Where domain ownership is genuinely ambiguous, the more recently synced policy source should win, which only works if every agent's last sync timestamp is queryable, not just assumed.
What the agent should actually say to the customer
The honest answer beats a confident guess. An agent that recognizes it may be contradicting a sibling system should tell the customer directly: I want to double check that against what you were told before I confirm it, rather than either repeating its own answer more forcefully or silently changing its answer to match what the customer reported hearing elsewhere, which just teaches customers that whichever agent they talk to last is the one that caves. This is a different failure mode from a human agent and an AI agent giving different answers, where the human's authority is usually the simpler tiebreaker.
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When the contradiction has to escalate instead of self resolve
Some categories should never be self arbitrated by either agent, no matter how confident the precedence rule is: anything involving a specific dollar amount already quoted, a legal or contractual commitment, or a safety related instruction. In those cases the correct behavior is an immediate human escalation with both agents' answers attached side by side, not a best guess resolution. This mirrors the caution already built into how teams handle two customers getting contradictory answers about the same transaction, where the cost of guessing wrong is asymmetric with the cost of a short delay.
Logging the collision even after it is resolved
Every live arbitration event, resolved automatically or escalated, should be logged as a distinct event type separate from a routine escalation, because a pattern of frequent collisions in the same domain is the clearest signal that the underlying shared source of truth fix needs to be prioritized sooner rather than later. Treat the arbitration log as the early warning system for the architectural fix, not just a record of individual incidents.
FAQ
Should the customer ever be told which agent was wrong?
Once resolved, yes, in plain terms and without assigning blame to a named system the customer will not recognize. The goal is closing the loop honestly, not protecting either agent's reputation internally.
Does this protocol apply to a vendor's agent talking to your agent as well?
No, that is a different design problem covered by how you structure an agent to agent handoff with another company's AI agent. This protocol is specifically for two agents you own contradicting each other.

