# Contracts under Moral Hazard and Adverse Selection

arXiv: https://arxiv.org/abs/2010.06742 · HTML: https://mlsanity.com/paper/2010.06742/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2020.

## Built on by (most cited first, 21 of 21)

- [The Sample Complexity of Online Contract Design](https://mlsanity.com/paper/2211.05732/) (2022)
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- [Principal-Agent Hypothesis Testing](https://mlsanity.com/paper/2205.06812/) (2022)
- [Deep Contract Design via Discontinuous Networks](https://mlsanity.com/paper/2307.02318/) (2023)
- [Online Learning in a Creator Economy](https://mlsanity.com/paper/2305.11381/) (2023)
- [Delegating Data Collection in Decentralized Machine Learning](https://mlsanity.com/paper/2309.01837/) (2023)
- [Learning to Incentivize Information Acquisition: Proper Scoring Rules Meet Principal-Agent Model](https://mlsanity.com/paper/2303.08613/) (2023)
- [Are Bounded Contracts Learnable and Approximately Optimal?](https://mlsanity.com/paper/2402.14486/) (2024)
- [Learning Optimal Contracts: How to Exploit Small Action Spaces](https://mlsanity.com/paper/2309.09801/) (2023)
- [Contractual Reinforcement Learning: Pulling Arms with Invisible Hands](https://mlsanity.com/paper/2407.01458/) (2024)
- [Emergent Risk Awareness in Rational Agents under Resource Constraints](https://mlsanity.com/paper/2505.23436/) (2025)
- [Optimal Scoring Rule Design under Partial Knowledge](https://mlsanity.com/paper/2107.07420/) (2021)
- [Learning to Mitigate Externalities: the Coase Theorem with Hindsight Rationality](https://mlsanity.com/paper/2406.19824/) (2024)
- [The Pseudo-Dimension of Contracts](https://mlsanity.com/paper/2501.14474/) (2025)
- [Fair Contracts in Principal-Agent Games with Heterogeneous Types](https://mlsanity.com/paper/2506.15887/) (2025)
- [What's a Credit Worth? A Market Framework for Attribution-Aware Compensation in Generative Music](https://mlsanity.com/paper/2607.00641/) (2026)
- [The Sample Complexity of Online Strategic Decision Making with Information Asymmetry and Knowledge Transportability](https://mlsanity.com/paper/2506.09940/) (2025)
- [LMM-Incentive: Large Multimodal Model-based Incentive Design for User-Generated Content in Web 3.0](https://mlsanity.com/paper/2510.04765/) (2025)
- [The Optimal Sample Complexity of Linear Contracts](https://mlsanity.com/paper/2601.01496/) (2026)
- [Minimax-Optimal Online Contract Design with Unrestricted Bounded Contracts](https://mlsanity.com/paper/2609.20353/) (2026)

## Abstract (arXiv)

In the classical principal-agent problem, a principal must design a contract to incentivize an agent to perform an action on behalf of the principal. We study the classical principal-agent problem in a setting where the agent can be of one of several types (affecting the outcome of actions they might take). This combines the contract theory phenomena of "moral hazard" (incomplete information about actions) with that of "adverse selection" (incomplete information about types). We examine this problem through the computational lens. We show that in this setting it is APX-hard to compute either the profit-maximizing single contract or the profit-maximizing menu of contracts (as opposed to in the absence of types, where one can efficiently compute the optimal contract). We then show that the performance of the best linear contract scales especially well in the number of types: if agent has n available actions and T possible types, the best linear contract achieves an O(nlog T) approximation of the best possible profit. Finally, we apply our framework to prove tight worst-case approximation bounds between a variety of benchmarks of mechanisms for the principal.