Information-trigger contracts in Principal-agent models with bonus caps

Nanxi Zhang is an assistant professor at Ivey business school, University of Western Ontario. She obtained her PhD from Shanghai University of Finance and Economics. Her research interest includes revenue management and contract theory.

We study a risk-neutral principal–agent moral-hazard problem with individual rationality (IR), incentive compatibility (IC), and limited liability. The existing literature analyses this setting largely under two auxiliary premises—an IR-binding contract and the validity of the first-order approach (FOA). These restrictions facilitate the analysis but narrow the scope of analysis and rule out economically meaningful cases, including scenarios in which the first-best effort is not attainable and FOA is invalid.

A key difficulty in the IR-nonbinding case under this problem is the nonexistence of optimal contracts.

In order to address this issue, we extend the discussion by imposing an exogenous cap on the contract, which restores the existence of optimal solutions when IR is nonbinding.

Bonus cap is not new to literature and has been justified in previous literature like \cite{chi2025optimal}.

Under this capped model, we show that every optimal contract takes an information-trigger form: the agent receives the maximal bonus whenever a likelihood-ratio statistic of the realized outcome crosses a threshold and receives the minimal payment otherwise. This contract rewards the agent only when the outcome provides sufficiently strong evidence of high effort, generalizing the classical quota–bonus contract.

Our analysis does not rely on FOA. Instead, we develop a minimax relaxation for the original moral hazard problem that collapses the continuous-action problem to a two-action comparison, allowing us to analyze the optimal contract even when IR is nonbinding.