The Value of Information in Binary, Limited-Liability Principal-Agent Games with Unobservable Outcome

Many applications in accounting, economics, and business, employ binary principal–agent game wherein the work-averse, risk-averse agent takes unobservable actions that determine stochastically the mutually-observable outcome on the basis of which the principal designs the incentives of the agent paid before the principal collects his share. In this paper we study a binary game when the outcome is unobservable and when the agent is protected by limited liability. The principal bases the incentives on the imperfectly audited report of the agent on outcome subject to the constraint that no payment can fall below the agent’s limited liability. The most interesting results are that we find that limited liability does not guarantee a higher expected payoff to the agent since the principal can use additional signal to fine-tune the contract, and that, as a result, there is a demand for a post-outcome signal that is non-informative in Holmstrom’s (1979) sense. The binary setting clearly shows the similarities in contract’s design of three different contracts: a contract based on mutually-observable outcome (our benchmark contract), a renegotiation-proof contract that induces the agent to report the truth, and a contract based on a report that can be manipulated by the agent. In particular, when limited liability is low (high), the renegotiation-proof contract is similar to a contract based on mutually-observable outcome (managed report).