# Learning to Mitigate Externalities: the Coase Theorem with Hindsight Rationality

arXiv: https://arxiv.org/abs/2406.19824 · HTML: https://mlsanity.com/paper/2406.19824/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 64 references that are in the map.
- First posted on arXiv 28 Jun 2024.

## Builds on (most cited first, 28 of 28)

- [Introduction to Multi-Armed Bandits](https://mlsanity.com/paper/1904.07272/) (2019)
- [Social Learning in Multi Agent Multi Armed Bandits](https://mlsanity.com/paper/1910.02100/) (2019)
- [SIC-MMAB: Synchronisation Involves Communication in Multiplayer Multi-Armed Bandits](https://mlsanity.com/paper/1809.08151/) (2018)
- [Bayesian Exploration: Incentivizing Exploration in Bayesian Games](https://mlsanity.com/paper/1602.07570/) (2016)
- [The Sample Complexity of Online Contract Design](https://mlsanity.com/paper/2211.05732/) (2022)
- [Learning to Bid Without Knowing your Value](https://mlsanity.com/paper/1711.01333/) (2017)
- [Simple versus Optimal Contracts](https://mlsanity.com/paper/1808.03713/) (2018)
- [Contracting with a Learning Agent](https://mlsanity.com/paper/2401.16198/) (2024)
- [Contracts under Moral Hazard and Adverse Selection](https://mlsanity.com/paper/2010.06742/) (2020)
- [A survey on multi-player bandits](https://mlsanity.com/paper/2211.16275/) (2022)
- [Sequential Information Design: Markov Persuasion Process and Its Efficient Reinforcement Learning](https://mlsanity.com/paper/2202.10678/) (2022)
- [Principal-Agent Reward Shaping in MDPs](https://mlsanity.com/paper/2401.00298/) (2023)
- [Incentivized Learning in Principal-Agent Bandit Games](https://mlsanity.com/paper/2403.03811/) (2024)
- [Exploration and Incentives in Reinforcement Learning](https://mlsanity.com/paper/2103.00360/) (2021)
- [Efficient Stackelberg Strategies for Finitely Repeated Games](https://mlsanity.com/paper/2207.04192/) (2022)
- [Sequential Information Design: Learning to Persuade in the Dark](https://mlsanity.com/paper/2209.03927/) (2022)
- [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)
- [Repeated Principal-Agent Games with Unobserved Agent Rewards and Perfect-Knowledge Agents](https://mlsanity.com/paper/2304.07407/) (2023)
- [Bandit Learning with Positive Externalities](https://mlsanity.com/paper/1802.05693/) (2018)
- [Estimating and Incentivizing Imperfect-Knowledge Agents with Hidden Rewards](https://mlsanity.com/paper/2308.06717/) (2023)
- [Impact of Decentralized Learning on Player Utilities in Stackelberg Games](https://mlsanity.com/paper/2403.00188/) (2024)
- [Coordinated Dynamic Bidding in Repeated Second-Price Auctions with Budgets](https://mlsanity.com/paper/2306.07709/) (2023)
- [Actions Speak What You Want: Provably Sample-Efficient Reinforcement Learning of the Quantal Stackelberg Equilibrium from Strategic Feedbacks](https://mlsanity.com/paper/2307.14085/) (2023)
- [Contract Design With Safety Inspections](https://mlsanity.com/paper/2311.02537/) (2023)
- [Robust and Performance Incentivizing Algorithms for Multi-Armed Bandits with Strategic Agents](https://mlsanity.com/paper/2312.07929/) (2023)
- [Learning Optimal Tax Design in Nonatomic Congestion Games](https://mlsanity.com/paper/2402.07437/) (2024)
- [Fair Allocation in Dynamic Mechanism Design](https://mlsanity.com/paper/2406.00147/) (2024)

## Built on by (most cited first, 3 of 3)

- [Principal-Agent Bandit Games with Self-Interested and Exploratory Learning Agents](https://mlsanity.com/paper/2412.16318/) (2024)
- [Learning to Incentivize in Repeated Principal-Agent Problems with Adversarial Agent Arrivals](https://mlsanity.com/paper/2505.23124/) (2025)
- [Microeconomic Foundations of Multi-Agent Learning](https://mlsanity.com/paper/2601.03451/) (2026)

## Abstract (arXiv)

In economic theory, the concept of externality refers to any indirect effect resulting from an interaction between players that affects the social welfare. Most of the models within which externality has been studied assume that agents have perfect knowledge of their environment and preferences. This is a major hindrance to the practical implementation of many proposed solutions. To address this issue, we consider a two-player bandit setting where the actions of one of the players affect the other player and we extend the Coase theorem [Coase, 1960]. This result shows that the optimal approach for maximizing the social welfare in the presence of externality is to establish property rights, i.e., enable transfers and bargaining between the players. Our work removes the classical assumption that bargainers possess perfect knowledge of the underlying game. We first demonstrate that in the absence of property rights, the social welfare breaks down. We then design a policy for the players which allows them to learn a bargaining strategy which maximizes the total welfare, recovering the Coase theorem under uncertainty.