Ex-post moral hazard and manipulation-proof contracts

TL;DR

This paper explores the balance between incentivizing effort and preventing profit manipulation in contracts, revealing that the optimal contract's robustness depends on the manipulation technology and output distribution.

Contribution

It introduces a formal model analyzing ex-post moral hazard and identifies conditions under which contracts are manipulation-proof or susceptible to manipulation.

Findings

Manipulation-proofness depends on the interaction between manipulation technology and output distribution.

Linear manipulation technology always allows for manipulation-proof contracts.

Convex manipulation technology can lead to manipulations in equilibrium.

Abstract

We examine the trade-off between the provision of incentives to exert costly effort (ex-ante moral hazard) and the incentives needed to prevent the agent from manipulating the profit observed by the principal (ex-post moral hazard). Formally, we build a model of two-stage hidden actions where the agent can both influence the expected revenue of a business and manipulate its observed profit. We show that manipulation-proofness is sensitive to the interaction between the manipulation technology and the probability distribution of the stochastic output. The optimal contract is manipulation-proof whenever the manipulation technology is linear. However, a convex manipulation technology sometimes leads to contracts with manipulations in equilibrium. Whenever the distribution satisfies the monotone likelihood ratio property, we can always find a manipulation technology for which the optimal contract is not manipulation-proof.