Comparisons of Experiments in Moral Hazard Problems

I use a novel geometric approach to compare information in moral hazard problems. I study three nested geometric orders on information, namely the column space, the conic span, and the zonotope orders. The orders are defined by the inclusion of the column space, the conic span, and the zonotope of the matrices representing the experiments. For each order, I establish four equivalent characterizations of the orders, (i) inclusion of feasible state-dependent utility sets, (ii) matrix factorizations, (iii) posterior belief distributions, and (iv) improved incentives in certain moral hazard problems. The column space order characterizes the comparisons of implementability in all moral hazard problems. The conic span order characterizes the comparisons of costs in all moral hazard problems with a risk neutral agent and limited liability. The zonotope order characterizes the comparisons of costs in all moral hazard problems when the agent can have any utility exhibiting risk aversion.