# Social Gym and SPaRTan: Benchmarking and Improving LLM Social Reasoning via Multi-Agent Game Tournaments

arXiv: https://arxiv.org/abs/2608.09128 · HTML: https://mlsanity.com/paper/2608.09128/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 16 of its 55 references that are in the map.
- First posted on arXiv 10 Aug 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)

## Builds on (most cited first, 16 of 16)

- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Voyager: An Open-Ended Embodied Agent with Large Language Models](https://mlsanity.com/paper/2305.16291/) (2023)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [SOTOPIA: Interactive Evaluation for Social Intelligence in Language Agents](https://mlsanity.com/paper/2310.11667/) (2023)
- [Large Language Models Fail on Trivial Alterations to Theory-of-Mind Tasks](https://mlsanity.com/paper/2302.08399/) (2023)
- [Exploring Large Language Models for Communication Games: An Empirical Study on Werewolf](https://mlsanity.com/paper/2309.04658/) (2023)
- [Evaluating Large Language Models in Theory of Mind Tasks](https://mlsanity.com/paper/2302.02083/) (2023)
- [AgentSociety: Large-Scale Simulation of LLM-Driven Generative Agents Advances Understanding of Human Behaviors and Society](https://mlsanity.com/paper/2502.08691/) (2025)
- [GTBench: Uncovering the Strategic Reasoning Limitations of LLMs via Game-Theoretic Evaluations](https://mlsanity.com/paper/2402.12348/) (2024)
- [SPIRAL: Self-Play on Zero-Sum Games Incentivizes Reasoning via Multi-Agent Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2506.24119/) (2025)
- [LLM-Based Agent Society Investigation: Collaboration and Confrontation in Avalon Gameplay](https://mlsanity.com/paper/2310.14985/) (2023)
- [Is this the real life? Is this just fantasy? The Misleading Success of Simulating Social Interactions With LLMs](https://mlsanity.com/paper/2403.05020/) (2024)
- [AvalonBench: Evaluating LLMs Playing the Game of Avalon](https://mlsanity.com/paper/2310.05036/) (2023)
- [TextArena](https://mlsanity.com/paper/2504.11442/) (2025)
- [SOTOPIA-TOM: Evaluating Privacy and Information Management in Multi-Agent Interaction with Theory of Mind](https://mlsanity.com/paper/2605.02307/) (2026)
- [Imperfectly Cooperative Human-AI Interactions: Comparing the Impacts of Human and AI Attributes in Simulated and User Studies](https://mlsanity.com/paper/2604.15607/) (2026)

## Built on by (most cited first, 2 of 2)

- [S3Gym: Can LLMs Turn Self-Testing and Self-Judging into Self-Improvement?](https://mlsanity.com/paper/2608.31100/) (2026)
- [What Makes a Social Agent's Interactions Effective? Learning from Verifiable Outcomes in Paired Worlds](https://mlsanity.com/paper/2610.20195/) (2026)

## Abstract (arXiv)

LLM agents are increasingly deployed in multi-agent social settings where they must cooperate, negotiate, and adapt to other agents. Measuring and improving these social skills is hard because, unlike math or logic, social interaction offers no objective ground truth: evaluations fall back on LLM judges, which are costly, subjective, and noisy, and models get no reliable signal to learn from. To address both, we first introduce Social Gym, an environment of 21 multi-agent social games (e.g., Werewolves, Resistance, Spyfall) whose rule-decided outcomes make agent performance verifiable and objective, with an Elo tournament that produces a cross-game leaderboard. Benchmarking experiments show that while GPT-5-mini tops the leaderboard, no model excels at all games uniformly or in all game roles, pointing to limitations of social reasoning. Motivated by this, we additionally propose SPaRTan (Self-Play and Reflect-Transfer), a training-free self-improvement loop: a model plays a game, reflects on its trajectories and their outcomes to produce a transferable playbook, and applies that playbook in subsequent games. Our results show that SPaRTan playbooks help GPT-5-mini agents level their performance on weaker roles, but largely do not improve Qwen3-32B's performance. Together, Social Gym and SPaRTan offer a reproducible, verifiable foundation for measuring and improving LLM social reasoning without weight updates.