Final answer:
The greatest risk of liability for an agent occurs in the context of an undisclosed principal and an authorized contract because the third party is unaware of dealing with an agent, which may lead to claims against the agent if disputes arise.
Step-by-step explanation:
The scenario in which the agent is exposed to the greatest risk of liability is when there is an undisclosed principal and an authorized contract. In such cases, third parties are unaware that they are dealing with an agent because the principal's identity is not revealed. If a dispute arises out of the contract, the third party may hold the agent liable because they believed they were dealing directly with the agent as the principal party. This increased risk comes from the fact that the third party was not informed of the principal-agent relationship at the time of the contract, potentially leading to claims of deception or fraud.