# Adaptive Punishment for Cooperation in Mixed-Motive Games

arXiv: https://arxiv.org/abs/2605.24516 · HTML: https://mlsanity.com/paper/2605.24516/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 26 references that are in the map.
- First posted on arXiv 23 May 2026.

## Builds on (most cited first, 15 of 15)

- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [Value-Decomposition Networks For Cooperative Multi-Agent Learning](https://mlsanity.com/paper/1706.05296/) (2017)
- [Learning with Opponent-Learning Awareness](https://mlsanity.com/paper/1709.04326/) (2017)
- [Inequity aversion improves cooperation in intertemporal social dilemmas](https://mlsanity.com/paper/1803.08884/) (2018)
- [Scalable Evaluation of Multi-Agent Reinforcement Learning with Melting Pot](https://mlsanity.com/paper/2107.06857/) (2021)
- [A multi-agent reinforcement learning model of common-pool resource appropriation](https://mlsanity.com/paper/1707.06600/) (2017)
- [Maintaining cooperation in complex social dilemmas using deep reinforcement learning](https://mlsanity.com/paper/1707.01068/) (2017)
- [Prosocial learning agents solve generalized Stag Hunts better than selfish ones](https://mlsanity.com/paper/1709.02865/) (2017)
- [AdaSociety: An Adaptive Environment with Social Structures for Multi-Agent Decision-Making](https://mlsanity.com/paper/2411.03865/) (2024)
- [D3C: Reducing the Price of Anarchy in Multi-Agent Learning](https://mlsanity.com/paper/2010.00575/) (2020)
- [Efficient Adaptation in Mixed-Motive Environments via Hierarchical Opponent Modeling and Planning](https://mlsanity.com/paper/2406.08002/) (2024)
- [Learning to Balance Altruism and Self-interest Based on Empathy in Mixed-Motive Games](https://mlsanity.com/paper/2410.07863/) (2024)
- [The emergence of division of labor through decentralized social sanctioning](https://mlsanity.com/paper/2208.05568/) (2022)
- [Investigating the Impact of Direct Punishment on the Emergence of Cooperation in Multi-Agent Reinforcement Learning Systems](https://mlsanity.com/paper/2301.08278/) (2023)

## Abstract (arXiv)

Mixed-motive scenarios are ubiquitous in real-world multi-agent interactions, where self-interested agents often defect for immediate rewards, overlooking the potential of altruistic cooperation to improve long-term gains and collective welfare. Peer punishment can deter defection, but as costly second-order altruism, its persistent imposition may undermine the punisher's interests. Existing approaches often struggle to effectively implement punishment to promote cooperation. To balance the efficacy and cost of punishment, we propose Adaptive Punishment for Cooperation (APC), a distributed method that determines punishment intensity based on both a dynamic punishment probability and the severity of defection. This dynamic probability substantially reduces costly and ineffective punishment while also promotes cooperation. To accurately assess defection and its severity, we use a defection awareness module, whose learning is guided by game reward. Theoretical analysis and empirical results show APC performs effectively in iterated public goods game. Empirically, APC also significantly outperforms existing baselines across sequential social dilemmas, learning rational and effective punishment policies that foster cooperation by strategically deterring defection.