Risk-Sharing Partners with Bilateral Moral Hazard and Balanced Budgets

In this paper we study the problem of optimal risk sharing in a model of partnership with bilateral moral hazard and balanced budgets. In our model, there are two risk-averse agents who engage in independent productions and share the aggregate output. Each agent's production requires an effort which is unobservable to the other agent. Moreover, the agents face a resource constraint which imposes that their total consumption cannot exceed the aggregate output. We show that with bilateral moral hazard, the dependence of consumptions on outputs still occurs only through the likelihood ratios, as in standard agency models. We give sufficient conditions for a first-order approach to bilateral incentive compatibility, which allows us to derive some monotonicity results concerning the optimal trading schemes. We take a computational approach to find that the budget balancing constraint may significantly affect the structure of optimal tradings. For instance, when at least one non-negativity constraint is binding, an agent is required to make a higher effort when he is entitled to a higher expected utility, whereas the converse holds in the case where no non-negativity constraint binds. We examine how the equilibrium trades differ with dominant strategy and Nash incentive compatibility.