Optimal Contracts under Generalized Verifiability Correspondences

Before playing a game, the players may sign a contract that prescibes not to take some actions. Following the methodology introduced in Bernheim and Whinston (1998), henceforth BW, this paper models verifiability as a correspondence mapping actually played actions that cannot be ruled out by a court. BW characterize optimal contracts in various settings both static and sequential, and show instances where optimal contracts must necessarily leave some verifiable prescriptions unspecified. This paper focuses on static settings. We extend the line of research of BW by considering also non-partitional and non-product correspondences, and by introducing different liability regimes in the framework. A complete characterization of optimal contracts is derived. We identify instances where, because of liability constraints, the optimal contracts must explicitely include unverifiable prescriptions. In some cases, the optimal outcome may be achieved only by signing a contract that cannot be enforced. Our analysis may be of some relevance for the foundations of incomplete contracts, as it shows that it is not necessarily the case that the players should sign an incomplete contract when complete contracts are unenforceable.