Games Suppliers and Producers Play : Upstream and Downstream Moral Hazard with Unverifiable Input Quality

We pin down the optimal relational contract between an input supplier and a final goods producer given a framework of bilateral moral hazard with variable but non-verifiable input quality. Given the inability of third parties to verify input quality, each party has an incentive to cheat the other by making a false claim about input quality. We derive the contract which (a) induces honest behavior and brings about the Pareto superior first-best outcome for the widest possible range of exogenous parameters, and (b) maximizes the Nash product of both parties payoffs subject to incentive compatibility. An interesting feature of the optimal contract is that it is of a fixed-price variety with the final producer paying the supplier the same transfer price whether he has been supplied a high or low quality input when the agreement was to supply high quality. This contrasts with the traditional incomplete contracting literature where fixed-price contracts (eg, payment of a fixed wage to workers) was optimal only in the full information case while ours is a case of incomplete information. The contrast is rooted both in the bilateral nature of the moral hazard we consider and in the repeated game framework we use. We also pinpoint the exact transfer price in the optimal contract, which may vary for different parameter ranges, and show how the best contract differs from the optimal contract under complete contracting.