# Simple versus Optimal Contracts

arXiv: https://arxiv.org/abs/1808.03713 · HTML: https://mlsanity.com/paper/1808.03713/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Aug 2018.

## Built on by (most cited first, 30 of 33)

- [The Sample Complexity of Online Contract Design](https://mlsanity.com/paper/2211.05732/) (2022)
- [Stateful Strategic Regression](https://mlsanity.com/paper/2106.03827/) (2021)
- [Contracting with a Learning Agent](https://mlsanity.com/paper/2401.16198/) (2024)
- [Principal-Agent Hypothesis Testing](https://mlsanity.com/paper/2205.06812/) (2022)
- [Deep Contract Design via Discontinuous Networks](https://mlsanity.com/paper/2307.02318/) (2023)
- [Delegated Classification](https://mlsanity.com/paper/2306.11475/) (2023)
- [Incentivizing Quality Text Generation via Statistical Contracts](https://mlsanity.com/paper/2406.11118/) (2024)
- [Principal-Agent Reinforcement Learning: Orchestrating AI Agents with Contracts](https://mlsanity.com/paper/2407.18074/) (2024)
- [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)
- [Learning in Online Principal-Agent Interactions: The Power of Menus](https://mlsanity.com/paper/2312.09869/) (2023)
- [Repeated Contracting with Multiple Non-Myopic Agents: Policy Regret and Limited Liability](https://mlsanity.com/paper/2402.17108/) (2024)
- [Harnessing the Continuous Structure: Utilizing the First-order Approach in Online Contract Design](https://mlsanity.com/paper/2403.07143/) (2024)
- [Robust and Performance Incentivizing Algorithms for Multi-Armed Bandits with Strategic Agents](https://mlsanity.com/paper/2312.07929/) (2023)
- [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)
- [Regret Minimization for Piecewise Linear Rewards: Contracts, Auctions, and Beyond](https://mlsanity.com/paper/2503.01701/) (2025)
- [The Backfiring Effect of Weak AI Safety Regulation](https://mlsanity.com/paper/2503.20848/) (2025)
- [Operationalizing Counterfactual Metrics: Incentives, Ranking, and Information Asymmetry](https://mlsanity.com/paper/2305.14595/) (2023)
- [Learning to Incentivize in Repeated Principal-Agent Problems with Adversarial Agent Arrivals](https://mlsanity.com/paper/2505.23124/) (2025)
- [Reward Shaping for (Inference-Time) Alignment: A Stackelberg Game Perspective](https://mlsanity.com/paper/2602.02572/) (2026)
- [Fair Contracts in Principal-Agent Games with Heterogeneous Types](https://mlsanity.com/paper/2506.15887/) (2025)
- [Disinformation, Stochastic Harm, and Costly Effort: A Principal-Agent Analysis of Regulating Social Media Platforms](https://mlsanity.com/paper/2106.09847/) (2021)
- [Learning Under Moral Hazard with Instrumental Regression and Generalized Method of Moments](https://mlsanity.com/paper/2405.20642/) (2024)
- [Incentivizing High-Quality Human Annotations with Golden Questions](https://mlsanity.com/paper/2505.19134/) (2025)
- [Scalable Principal-Agent Contract Design via Gradient-Based Optimization](https://mlsanity.com/paper/2510.21177/) (2025)

## Abstract (arXiv)

We consider the classic principal-agent model of contract theory, in which a principal designs an outcome-dependent compensation scheme to incentivize an agent to take a costly and unobservable action. When all of the model parameters---including the full distribution over principal rewards resulting from each agent action---are known to the designer, an optimal contract can in principle be computed by linear programming. In addition to their demanding informational requirements, such optimal contracts are often complex and unintuitive, and do not resemble contracts used in practice. This paper examines contract theory through the theoretical computer science lens, with the goal of developing novel theory to explain and justify the prevalence of relatively simple contracts, such as linear (pure commission) contracts. First, we consider the case where the principal knows only the first moment of each action's reward distribution, and we prove that linear contracts are guaranteed to be worst-case optimal, ranging over all reward distributions consistent with the given moments. Second, we study linear contracts from a worst-case approximation perspective, and prove several tight parameterized approximation bounds.