# EquiMem: Calibrating Shared Memory in Multi-Agent Debate via Game-Theoretic Equilibrium

arXiv: https://arxiv.org/abs/2605.09278 · HTML: https://mlsanity.com/paper/2605.09278/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Agent memory systems, one of 16 directions in LLM agents and tool use.
- Builds on 79 of its 97 references that are in the map.
- First posted on arXiv 10 May 2026.

## Placed in

- LLM agents and tool use / [Agent memory systems](https://mlsanity.com/agents/agent-memory-systems/)

## Builds on (most cited first, 30 of 79)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Generative Agents: Interactive Simulacra of Human Behavior](https://mlsanity.com/paper/2304.03442/) (2023)
- [Retrieval-Augmented Generation for Large Language Models: A Survey](https://mlsanity.com/paper/2312.10997/) (2023)
- [Voyager: An Open-Ended Embodied Agent with Large Language Models](https://mlsanity.com/paper/2305.16291/) (2023)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [MetaGPT: Meta Programming for A Multi-Agent Collaborative Framework](https://mlsanity.com/paper/2308.00352/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [MemGPT: Towards LLMs as Operating Systems](https://mlsanity.com/paper/2310.08560/) (2023)
- [WebShop: Towards Scalable Real-World Web Interaction with Grounded Language Agents](https://mlsanity.com/paper/2207.01206/) (2022)
- [ALFWorld: Aligning Text and Embodied Environments for Interactive Learning](https://mlsanity.com/paper/2010.03768/) (2020)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [A-MEM: Agentic Memory for LLM Agents](https://mlsanity.com/paper/2502.12110/) (2025)
- [Towards Understanding Sycophancy in Language Models](https://mlsanity.com/paper/2310.13548/) (2023)
- [Red Teaming Language Models with Language Models](https://mlsanity.com/paper/2202.03286/) (2022)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [Evaluating Very Long-Term Conversational Memory of LLM Agents](https://mlsanity.com/paper/2402.17753/) (2024)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [Mem0: Building Production-Ready AI Agents with Scalable Long-Term Memory](https://mlsanity.com/paper/2504.19413/) (2025)
- [ChatEval: Towards Better LLM-based Evaluators through Multi-Agent Debate](https://mlsanity.com/paper/2308.07201/) (2023)
- [A Survey on the Memory Mechanism of Large Language Model based Agents](https://mlsanity.com/paper/2404.13501/) (2024)
- [AgentVerse: Facilitating Multi-Agent Collaboration and Exploring Emergent Behaviors](https://mlsanity.com/paper/2308.10848/) (2023)

## Built on by (most cited first, 4 of 4)

- [SoK: When Safe Agents Fail Together: The Security of Multi Agent LLM Systems](https://mlsanity.com/paper/2609.00595/) (2026)
- [Uncertainty Quantification for LLM Agents: A Taxonomy, an Evaluation Protocol, and an Empirical Study](https://mlsanity.com/paper/2609.07395/) (2026)
- [When Correct Memory Goes Wrong: Fuzzing Persistent Memory Use in LLM Agents](https://mlsanity.com/paper/2609.38275/) (2026)
- [Understanding and Mitigating Inference-Time Overreliance Using Agentic Memory](https://mlsanity.com/paper/2610.07311/) (2026)

## Abstract (arXiv)

Multi-agent debate (MAD) systems increasingly rely on shared memory to support long-horizon reasoning, but this convenience opens a critical vulnerability: a single corrupted entry can contaminate the downstream memory-augmented reasoning, and debate alone fails to filter such errors. Existing safeguards filter entries via heuristics or LLM-based validation, yet they rely on AI judgments that share the same failure modes and overlook the cross-agent dynamics of MAD. We address this gap by formulating memory updating in MAD as a zero-trust memory game, in which no agent is assumed reliable and the game's equilibrium motivates a principled objective for calibrating memory influence. Guided by this objective, we propose EquiMem, an inference-time calibration mechanism that evaluates each update against the shared memory state and the memory already being used by other agents, using their existing retrieval queries and traversal paths as evidence of calibration. EquiMem instantiates this calibration for both embedding- and graph-based memory, and across diverse benchmarks, MAD frameworks, and memory architectures, it consistently outperforms existing safeguards, remains robust under adversarial agents, and incurs negligible inference overhead.