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

Multi-agent debate (MAD) improves the reasoning capabilities of large language models by having multiple agents iteratively refine their responses through discussion. However, MAD suffers from a critical vulnerability known as shared misconception: when a majority of agents initially converge on an incorrect answer, the debate process tends to amplify rather than correct the error. Existing methods primarily address peer skew but leave the agents' inherently biased concept priors unaddressed. To mitigate this systematic weakness, we propose R$^2$-MAD (Remember and Reweight for Multi-Agent Debate), a framework that equips agents with an experience memory accumulated from past debates. R$^2$-MAD intervenes on both failure modes through two complementary mechanisms: A debate-state-aware retrieval policy dynamically calibrates the concept prior by retrieving relevant historical evidence based on the current consensus level. Then these retrieved experiences provide a basis for estimating per-agent reliability, yielding confidence weights to modulate peer influence. Experiments on various benchmarks show that R$^2$-MAD achieves consistent improvements over existing single-agent and MAD baselines.

Memory benchmarks for LLM agents largely assume single-user settings, leaving shared assistants for hospitals, workplaces, campuses, and households understudied. In these deployments, multiple principals write to a common memory pool and query it under different roles, scopes, and relationships, so memory quality requires governance as well as recall. We introduce GateMem, a benchmark for multi-principal shared-memory agents. GateMem jointly evaluates utility for legitimate long-horizon requests with state updates, access control across contextual authorization boundaries, and agent-facing active forgetting after explicit deletion requests. It spans medical, office, education, and household domains, with long-form multi-party episodes, incremental memory injection, hidden checkpoints, structured judging, and leak-target annotations. Across diverse baselines and backbone models, no method simultaneously achieves strong utility, robust access control, and reliable forgetting. Long-context prompting often yields the best governance score at high token cost, while retrieval-based and external-memory methods reduce cost yet still leak unauthorized or deleted information. These results show current memory agents remain far from reliable shared institutional deployment.

Self-evolving multi-agent systems (MAS) have emerged as a promising route to LLM agents that continually improve from experience, with persistent memory at their foundation. However, existing designs almost exclusively adopt a centralized repository shared across agents, incurring communication and coordination overhead, raising privacy concerns, and collapsing agent diversity. We propose DecentMem, a decentralized memory framework in which each agent maintains its own dual-pool memory -- an exploitation pool of consolidated past trajectories and an exploration pool of LLM-generated candidates for unseen contexts. The two pools are reweighted online based on stage-wise feedback from an LLM-as-a-judge. Theoretically, we prove that this design guarantees global reachability of the solution space and achieves $O(\log T)$ cumulative regret, matching the stochastic bandit lower bound up to constants. In practice, across three MAS frameworks (AutoGen, DyLAN, AgentNet), three Qwen3 backbones (4B/8B/14B), two Gemma4 backbones (E2B/E4B) and five benchmarks spanning math, code, QA, and embodied tasks, DecentMem improves average accuracy by up to 23.8% over the strongest centralized memory baseline and by up to 52.5% over the no-memory baseline, while reducing token usage by up to 49%.