# Joint Industrial Organization & CICER Workshop - Rongzhu Ke

#### Wed, 09/20/2017 - 11:40am

#### Rongzhu Ke

Hong Kong Baptist University

#### 498 Uris Hall

*"Information-Trigger Contracts"*

We study the moral hazard problem where the principal and agent are both risk neutral with lower and upper bounds on agent compensation. We show the optimality of information-trigger contracts, where the agent receives the highest possible payment when the likelihood ratio is higher than a certain cut-off (trigger) and is otherwise paid the minimum. The optimality of this contract is intuitive in the binary-action case. By reformulating the original problem to a covariance (between likelihood ratio and payment) maximization problem while controlling the expected payment, we are able to generalize it to a compact action space. We demonstrate equivalence with a relaxed problem where the order of optimization is swapped to where the principal responds optimally given two distinct actions. Moreover, under additional monotonicity assumptions, we adapt our machinery to show the optimality of quota-bonus contracts. When output satisfies the monotone likelihood ratio property, optimality follows by directly leveraging the information-trigger structure. This requires no additional assumptions, such as monotonicity of the contract space or the validity of the first-order approach, which are common in the existing literature. We also provide weak conditions for the optimality quota-bonus contracts when we do assume monotonicity of the contract space.

Event Categories: Industrial Organization