We propose formal definitions of substitutes and complements for information in the context of decision making under uncertainty. A decision maker needs to take an action to maximize his expected utility. Two pieces of information are substitutes (complements) for the decision problem if the more the decision maker knows about one decreases (increases) his marginal value of learning the other. Interestingly, a special class of decision problems — prediction problems where the decision maker predicts the distribution of a random variable and is rewarded for his prediction according to a proper scoring rule — is complete for understanding the value of information, in the sense that every decision problem has an “equivalent” prediction problem where the value of information is the same. Using the understanding of informational substitutes and complements, we characterize the game-theoretic equilibria of strategic play in prediction markets for any market scoring rule.
This talk is based on joint work with Bo Waggoner.