# Altruism and Fair Objective in Mixed-Motive Markov games

arXiv: https://arxiv.org/abs/2602.08389 · HTML: https://mlsanity.com/paper/2602.08389/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 24 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Builds on (most cited first, 11 of 11)

- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [The Surprising Effectiveness of PPO in Cooperative, Multi-Agent Games](https://mlsanity.com/paper/2103.01955/) (2021)
- [Inequity aversion improves cooperation in intertemporal social dilemmas](https://mlsanity.com/paper/1803.08884/) (2018)
- [Learning Fairness in Multi-Agent Systems](https://mlsanity.com/paper/1910.14472/) (2019)
- [AI for Global Climate Cooperation: Modeling Global Climate Negotiations, Agreements, and Long-Term Cooperation in RICE-N](https://mlsanity.com/paper/2208.07004/) (2022)
- [Heterogeneous-Agent Mirror Learning: A Continuum of Solutions to Cooperative MARL](https://mlsanity.com/paper/2208.01682/) (2022)
- [Proportionally Fair Online Allocation of Public Goods with Predictions](https://mlsanity.com/paper/2209.15305/) (2022)
- [SocialJax: An Evaluation Suite for Multi-agent Reinforcement Learning in Sequential Social Dilemmas](https://mlsanity.com/paper/2503.14576/) (2025)
- [Role Play: Learning Adaptive Role-Specific Strategies in Multi-Agent Interactions](https://mlsanity.com/paper/2411.01166/) (2024)
- [Skill-Aligned Fairness in Multi-Agent Learning for Collaboration in Healthcare](https://mlsanity.com/paper/2508.18708/) (2025)
- [Harm Ratio: A Novel and Versatile Fairness Criterion](https://mlsanity.com/paper/2410.02977/) (2024)

## Built on by (most cited first, 1 of 1)

- [α-fair heterogeneous agent reinforcement learning](https://mlsanity.com/paper/2606.13076/) (2026)

## Abstract (arXiv)

Cooperation is fundamental for society's viability, as it enables the emergence of structure within heterogeneous groups that seek collective well-being. However, individuals are inclined to defect in order to benefit from the group's cooperation without contributing the associated costs, thus leading to unfair situations. In game theory, social dilemmas entail this dichotomy between individual interest and collective outcome. The most dominant approach to multi-agent cooperation is the utilitarian welfare which can produce efficient highly inequitable outcomes. This paper proposes a novel framework to foster fairer cooperation by replacing the standard utilitarian objective with Proportional Fairness. We introduce a fair altruistic utility for each agent, defined on the individual log-payoff space and derive the analytical conditions required to ensure cooperation in classic social dilemmas. We then extend this framework to sequential settings by defining a Fair Markov Game and deriving novel fair Actor-Critic algorithms to learn fair policies. Finally, we evaluate our method in various social dilemma environments.