Effects of Risk Aversion on the Value of Information in Two‐Action Decision Problems

This paper analyzes the value of information in a two‐action decision problem where a decision maker is deciding on whether to accept an uncertain investment. We investigate the effects of the decision maker's risk aversion function on the value of information in this setting. We analyze the value of perfect information and the value of partition information where a decision maker with deterministic initial wealth receives information specifying that the outcome lies within a subset of the domain. We show that if two decision makers reject the investment without the information, then the more risk‐averse decision maker will value information (both perfect and partition), less than the less risk averse one. On the other hand, if both decision makers initially accept the investment, or are indifferent to the investment without the information, then (i) the more risk‐averse decision maker will value perfect information higher than the less risk‐averse one, but (ii) this monotonicity result need not apply for the case of partition information. These results enable us to compare the value of information when decision makers have different risk aversion levels. They also hold when comparison of risk aversion is restricted only to a domain defined by the lottery.