Socially Efficient Approval Mechanisms with Signalling Costs

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We consider an approval problem in which an agent with a privately known continuous type always seeks approval, whereas an uninformed principal favours approval only if the agent's type exceeds a certain standard. The agent sends a report about his type that he can inflate under some increasing cost that has the single-crossing property. We study approval mechanisms without transfers that maximize the weighted average of the ex-ante agent's and receiver's payoffs. The rule that maximizes the principal's payoff is a threshold rule, however, such a rule induces high costs for the agent. We show that when the marginal signalling cost is strictly log-supermodular, the efficient approval mechanism is stochastic, introducing an approval probability that is continuous in the agent's type. We provide the necessary first-order conditions for the optimal reporting rule and probability of approval.