mlsanityData to 7 Oct 2026

Cooperative Multi-Agent Fairness and Equivariant Policies

arXiv 2106.05727 ↗First posted 10 Jun 2021cs.AI cs.LG cs.MAcited by 8

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Abstract (arXiv)

We study fairness through the lens of cooperative multi-agent learning. Our work is motivated by empirical evidence that naive maximization of team reward yields unfair outcomes for individual team members. To address fairness in multi-agent contexts, we introduce team fairness, a group-based fairness measure for multi-agent learning. We then prove that it is possible to enforce team fairness during policy optimization by transforming the team's joint policy into an equivariant map. We refer to our multi-agent learning strategy as Fairness through Equivariance (Fair-E) and demonstrate its effectiveness empirically. We then introduce Fairness through Equivariance Regularization (Fair-ER) as a soft-constraint version of Fair-E and show that it reaches higher levels of utility than Fair-E and fairer outcomes than non-equivariant policies. Finally, we present novel findings regarding the fairness-utility trade-off in multi-agent settings; showing that the magnitude of the trade-off is dependent on agent skill.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 29 of its 57 references that are in the map. First posted on arXiv 10 Jun 2021.

Builds on

29 of 57 references.

References · 29

  1. 2015Continuous control with deep reinforcement learningcited by 3,279
  2. 2016Equality of Opportunity in Supervised Learningcited by 2,000
  3. 2017Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environmentscited by 1,519
  4. 2014Certifying and removing disparate impactcited by 715
  5. 2016Inherent Trade-Offs in the Fair Determination of Risk Scorescited by 582
  6. 2016Learning to Communicate with Deep Multi-Agent Reinforcement Learningcited by 561
  7. 2017Algorithmic decision making and the cost of fairnesscited by 402
  8. 2019Emergent Tool Use From Multi-Agent Autocurriculacited by 308
  9. 2017Emergence of Grounded Compositional Language in Multi-Agent Populationscited by 257
  10. 2017Multi-agent Reinforcement Learning in Sequential Social Dilemmascited by 206
  11. 2018Delayed Impact of Fair Machine Learningcited by 183
  12. 2019Inherent Tradeoffs in Learning Fair Representationscited by 144
17 more
  1. 2017Equivariance Through Parameter-Sharingcited by 139
  2. 2018The Frontiers of Fairness in Machine Learningcited by 139
  3. 2018Inequity aversion improves cooperation in intertemporal social dilemmascited by 106
  4. 2016Fairness in Reinforcement Learningcited by 93
  5. 2020The AI Economist: Improving Equality and Productivity with AI-Driven Tax Policiescited by 75
  6. 2019Shapley Q-value: A Local Reward Approach to Solve Global Reward Gamescited by 71
  7. 2019Operationalizing Individual Fairness with Pairwise Fair Representationscited by 64
  8. 2020Learning Fair Policies in Multiobjective (Deep) Reinforcement Learning with Average and Discounted Rewardscited by 60
  9. 2019Algorithms for Fairness in Sequential Decision Makingcited by 53
  10. 2017Prosocial learning agents solve generalized Stag Hunts better than selfish onescited by 47
  11. 2019Learning Fairness in Multi-Agent Systemscited by 44
  12. 2020Learning Fair Policies in Decentralized Cooperative Multi-Agent Reinforcement Learningcited by 40
  13. 2021Shapley Counterfactual Credits for Multi-Agent Reinforcement Learningcited by 37
  14. 2018Evolving intrinsic motivations for altruistic behaviorcited by 30
  15. 2018Fair Algorithms for Learning in Allocation Problemscited by 29
  16. 2021Investigating Trade-offs in Utility, Fairness and Differential Privacy in Neural Networkscited by 17
  17. 2020Low-Bandwidth Communication Emerges Naturally in Multi-Agent Learning Systemscited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 0; 2024: 5; 2025: 1; 2026: 1.

8 papers.

  1. 2024Fairness in Reinforcement Learning: A Surveycited by 9
  2. 2024Cooperation and Fairness in Multi-Agent Reinforcement Learningcited by 5
  3. 2022Fairness in Multi-Agent Planningcited by 1
  4. 2024Temporal Fairness in Decision Making Problemscited by 1
  5. 2024Operationalising Rawlsian Ethics for Fairness in Norm-Learning Agentscited by 1
  6. 2024Learning in Multi-Objective Public Goods Games with Non-Linear Utilitiescited by 0
  7. 2025MAFE: Enabling Equitable Algorithm Design in Multi-Agent Multi-Stage Decision-Making Systemscited by 0
  8. 2026ACPO: Agent-Chained Policy Optimization for Multi-Agent Reinforcement Learningcited by 0