# Statistical physics of human cooperation

arXiv: https://arxiv.org/abs/1705.07161 · HTML: https://mlsanity.com/paper/1705.07161/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2017.

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

- [Multi-Agent, Human-Agent and Beyond: A Survey on Cooperation in Social Dilemmas](https://mlsanity.com/paper/2402.17270/) (2024)
- [Social physics in the age of artificial intelligence](https://mlsanity.com/paper/2603.16900/) (2026)
- [Integrated Design and Governance of Agentic AI Systems through Adaptive Information Modulation](https://mlsanity.com/paper/2409.10372/) (2024)
- [Evolutionary mechanisms that promote cooperation may not promote social welfare](https://mlsanity.com/paper/2408.05373/) (2024)
- [How large language models judge and influence human cooperation](https://mlsanity.com/paper/2507.00088/) (2025)
- [Can Media Act as a Soft Regulator of Safe AI Development? A Game Theoretical Analysis](https://mlsanity.com/paper/2509.02650/) (2025)
- [LLM Constitutional Multi-Agent Governance](https://mlsanity.com/paper/2603.13189/) (2026)
- [A Reputation Game Simulation: Emergent Social Phenomena from Information Theory](https://mlsanity.com/paper/2106.05414/) (2021)
- [A Quantum-like Model for Predicting Human Decisions in the Entangled Social Systems](https://mlsanity.com/paper/2111.13902/) (2021)
- [Understanding Emergent Behaviours in Multi-Agent Systems with Evolutionary Game Theory](https://mlsanity.com/paper/2205.07369/) (2022)
- [Intrinsic fluctuations of reinforcement learning promote cooperation](https://mlsanity.com/paper/2209.01013/) (2022)
- [Cooperative control of environmental extremes by artificial intelligent agents](https://mlsanity.com/paper/2212.02395/) (2022)
- [Calibration of Quantum Decision Theory: Aversion to Large Losses and Predictability of Probabilistic Choices](https://mlsanity.com/paper/2303.02028/) (2023)
- [Quantum Operation of Affective Artificial Intelligence](https://mlsanity.com/paper/2305.08112/) (2023)
- [Enhancing Cooperation through Selective Interaction and Long-term Experiences in Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2405.02654/) (2024)
- [PPO-ACT: Proximal Policy Optimization with Adversarial Curriculum Transfer for Spatial Public Goods Games](https://mlsanity.com/paper/2505.04302/) (2025)
- [Dynamic Evolution of Complex Networks: A Reinforcement Learning Approach Applying Evolutionary Games to Community Structure](https://mlsanity.com/paper/2506.17925/) (2025)
- [Q-Learning-Driven Adaptive Rewiring for Cooperative Control in Heterogeneous Networks](https://mlsanity.com/paper/2509.01057/) (2025)
- [Strategic commitments shape collective cybersecurity under AI inequality](https://mlsanity.com/paper/2605.09415/) (2026)
- [The evolutionary advantage of guilt: co-evolution of social and non-social guilt in structured populations](https://mlsanity.com/paper/2302.09859/) (2023)
- [Discriminatory or Samaritan -- which AI is needed for humanity? An Evolutionary Game Theory Analysis of Hybrid Human-AI populations](https://mlsanity.com/paper/2306.17747/) (2023)
- [Discrete Versus Continuous Algorithms in Dynamics of Affective Decision Making](https://mlsanity.com/paper/2309.00357/) (2023)
- [Evolutionary game theory: the mathematics of evolution and collective behaviours](https://mlsanity.com/paper/2311.14480/) (2023)
- [Network Alignment](https://mlsanity.com/paper/2504.11367/) (2025)
- [TUC-PPO: Team Utility-Constrained Proximal Policy Optimization for Spatial Public Goods Games](https://mlsanity.com/paper/2507.02675/) (2025)
- [Social welfare optimisation in well-mixed and structured populations](https://mlsanity.com/paper/2512.07453/) (2025)
- [Generating consensus and dissent on massive discussion platforms with a semantic-vector model](https://mlsanity.com/paper/2601.13932/) (2026)
- [Social welfare optimisation under institutional reward and punishment](https://mlsanity.com/paper/2605.31330/) (2026)
- [Co-evolution of social reward and punishment under institutional interventions](https://mlsanity.com/paper/2608.01183/) (2026)
- [An Evolutionary Computation Framework for Multi-Agent Q-Learning with Mean-Field Environmental Feedback](https://mlsanity.com/paper/2609.13253/) (2026)

## Abstract (arXiv)

Extensive cooperation among unrelated individuals is unique to humans, who often sacrifice personal benefits for the common good and work together to achieve what they are unable to execute alone. The evolutionary success of our species is indeed due, to a large degree, to our unparalleled other-regarding abilities. Yet, a comprehensive understanding of human cooperation remains a formidable challenge. Recent research in social science indicates that it is important to focus on the collective behavior that emerges as the result of the interactions among individuals, groups, and even societies. Non-equilibrium statistical physics, in particular Monte Carlo methods and the theory of collective behavior of interacting particles near phase transition points, has proven to be very valuable for understanding counterintuitive evolutionary outcomes. By studying models of human cooperation as classical spin models, a physicist can draw on familiar settings from statistical physics. However, unlike pairwise interactions among particles that typically govern solid-state physics systems, interactions among humans often involve group interactions, and they also involve a larger number of possible states even for the most simplified description of reality. The complexity of solutions therefore often surpasses that observed in physical systems. Here we review experimental and theoretical research that advances our understanding of human cooperation, focusing on spatial pattern formation, on the spatiotemporal dynamics of observed solutions, and on self-organization that may either promote or hinder socially favorable states.