Recent work has shown that, in the presence of moral hazard, balanced budget Nash equilibria in groups are not pareto-optimal. This work shows that when agents misperceive the effects of their actions on the joint outcome, there exist a set of sharing rules which balance the budget and lead to a...

Propensity score matching is a popular way to make causal inferences about a binary treatment in observational data. The validity of these methods depends on which variables are used to predict the propensity score. We ask: "Absent strong ignorability, what would be the effect of including an...