Contracting for Decision-Relevant Beliefs

Abstract

An expert may misreport her forecast to influence a decision she cares about. We study contracts that elicit both her belief about a verifiable state and her stake in a binary action. If every belief is possible at two distinct stakes, exact incentive compatibility prevents a belief-only mechanism from letting the action depend on the report. Asking about both belief and stake allows the action to respond, but may require implementation rent. For threshold rules, we show that minimum rent equals the cutoff's positive curvature weighted by the belief distribution. The principal therefore chooses a cutoff by balancing virtual surplus against the implementation rent of truthful reporting. We characterize the best cutoff rule and give sufficient conditions under which it is optimal even among randomized mechanisms.