# Improving Rationality in the Reasoning Process of Language Models through Self-playing Game

arXiv: https://arxiv.org/abs/2506.22920 · HTML: https://mlsanity.com/paper/2506.22920/

## Key facts

- Cited by 7 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 40 of its 54 references that are in the map.
- First posted on arXiv 28 Jun 2025.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- Synthetic data and self-improvement for LLMs / [Self-play RL for reasoning](https://mlsanity.com/synth/self-play-rl-for-reasoning/)

## Builds on (most cited first, 30 of 40)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [An Empirical Study of Catastrophic Forgetting in Large Language Models During Continual Fine-tuning](https://mlsanity.com/paper/2308.08747/) (2023)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs](https://mlsanity.com/paper/2406.18629/) (2024)
- [Exploring Large Language Models for Communication Games: An Empirical Study on Werewolf](https://mlsanity.com/paper/2309.04658/) (2023)
- [Automatically Correcting Large Language Models: Surveying the landscape of diverse self-correction strategies](https://mlsanity.com/paper/2308.03188/) (2023)
- [Self-Play Preference Optimization for Language Model Alignment](https://mlsanity.com/paper/2405.00675/) (2024)
- [Improving Language Model Negotiation with Self-Play and In-Context Learning from AI Feedback](https://mlsanity.com/paper/2305.10142/) (2023)
- [Teaching Large Language Models to Reason with Reinforcement Learning](https://mlsanity.com/paper/2403.04642/) (2024)
- [Language Agents with Reinforcement Learning for Strategic Play in the Werewolf Game](https://mlsanity.com/paper/2310.18940/) (2023)
- [Marco-o1: Towards Open Reasoning Models for Open-Ended Solutions](https://mlsanity.com/paper/2411.14405/) (2024)
- [O1 Replication Journey: A Strategic Progress Report -- Part 1](https://mlsanity.com/paper/2410.18982/) (2024)
- [Impact of Pretraining Term Frequencies on Few-Shot Reasoning](https://mlsanity.com/paper/2202.07206/) (2022)
- [The CoT Collection: Improving Zero-shot and Few-shot Learning of Language Models via Chain-of-Thought Fine-Tuning](https://mlsanity.com/paper/2305.14045/) (2023)

## Built on by (most cited first, 7 of 7)

- [WoW: Towards a World omniscient World model Through Embodied Interaction](https://mlsanity.com/paper/2509.22642/) (2025)
- [World Action Verifier: Self-Improving World Models via Forward-Inverse Asymmetry](https://mlsanity.com/paper/2604.01985/) (2026)
- [Beyond Majority Voting: Towards Fine-grained and More Reliable Reward Signal for Test-Time Reinforcement Learning](https://mlsanity.com/paper/2512.15146/) (2025)
- [SCALER:Synthetic Scalable Adaptive Learning Environment for Reasoning](https://mlsanity.com/paper/2601.04809/) (2026)
- [MOTIF: Multi-strategy Optimization via Turn-based Interactive Framework](https://mlsanity.com/paper/2508.03929/) (2025)
- [What Can You Do When You Have Zero Rewards During RL?](https://mlsanity.com/paper/2510.03971/) (2025)
- [Living the Novel: A System for Generating Self-Training Timeline-Aware Conversational Agents from Novels](https://mlsanity.com/paper/2512.07474/) (2025)

## Abstract (arXiv)

Large language models (LLMs) have demonstrated considerable reasoning abilities in various tasks such as mathematics and coding. However, recent studies indicate that even the best models lack true comprehension of their reasoning processes. In this paper, we explore how self-play can enhance the rationality of models in the reasoning process without supervision from humans or superior models. We design a Critic-Discernment Game(CDG) in which a prover first provides a solution to a given problem and is subsequently challenged by critiques of its solution. These critiques either aim to assist or mislead the prover. The objective of the prover is to maintain the correct answer when faced with misleading comments, while correcting errors in response to constructive feedback. Our experiments on tasks involving mathematical reasoning, stepwise error detection, self-correction, and long-chain reasoning demonstrate that CDG training can significantly improve the ability of well-aligned LLMs to comprehend their reasoning process.