An agent who has a linear utility function, which implies that the agent will choose between gambles strictly on the basis of their expected monetary value, is risk

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A linear utility function implies that the agent is risk-neutral, meaning that they are indifferent between a sure payment and a gamble with the same expected value. The agent's choices are solely based on the expected monetary value of the options. Risk aversion implies that the agent would choose a certain payment over a gamble with the same expected value, and risk preference implies that the agent would choose a gamble with a lower expected value over a certain payment.

An Agent Who Has a Linear Utility Function, Which Implies