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Belief-Driven Multi-Agent Collaboration via Approximate Perfect Bayesian Equilibrium for Social Simulation

Weiwei Fang, Lin Li, Kaize Shi, Yu Yang, Jianwei Zhang

Abstract

High-fidelity social simulation is pivotal for addressing complex Web societal challenges, yet it demands agents capable of authentically replicating the dynamic spectrum of human interaction. Current LLM-based multi-agent frameworks, however, predominantly adhere to static interaction topologies, failing to capture the fluid oscillation between cooperative knowledge synthesis and competitive critical reasoning seen in real-world scenarios. This rigidity often leads to unrealistic ``groupthink'' or unproductive deadlocks, undermining the credibility of simulations for decision support. To bridge this gap, we propose \textit{BEACOF}, a \textit{belief-driven adaptive collaboration framework} inspired by Perfect Bayesian Equilibrium (PBE). By modeling social interaction as a dynamic game of incomplete information, BEACOF rigorously addresses the circular dependency between collaboration type selection and capability estimation. Agents iteratively refine probabilistic beliefs about peer capabilities and autonomously modulate their collaboration strategy, thereby ensuring sequentially rational decisions under uncertainty. Validated across adversarial (judicial), open-ended (social) and mixed (medical) scenarios, BEACOF prevents coordination failures and fosters robust convergence toward high-quality solutions, demonstrating superior potential for reliable social simulation. Source codes and datasets are publicly released at: https://github.com/WUT-IDEA/BEACOF.

Belief-Driven Multi-Agent Collaboration via Approximate Perfect Bayesian Equilibrium for Social Simulation

Abstract

High-fidelity social simulation is pivotal for addressing complex Web societal challenges, yet it demands agents capable of authentically replicating the dynamic spectrum of human interaction. Current LLM-based multi-agent frameworks, however, predominantly adhere to static interaction topologies, failing to capture the fluid oscillation between cooperative knowledge synthesis and competitive critical reasoning seen in real-world scenarios. This rigidity often leads to unrealistic ``groupthink'' or unproductive deadlocks, undermining the credibility of simulations for decision support. To bridge this gap, we propose \textit{BEACOF}, a \textit{belief-driven adaptive collaboration framework} inspired by Perfect Bayesian Equilibrium (PBE). By modeling social interaction as a dynamic game of incomplete information, BEACOF rigorously addresses the circular dependency between collaboration type selection and capability estimation. Agents iteratively refine probabilistic beliefs about peer capabilities and autonomously modulate their collaboration strategy, thereby ensuring sequentially rational decisions under uncertainty. Validated across adversarial (judicial), open-ended (social) and mixed (medical) scenarios, BEACOF prevents coordination failures and fosters robust convergence toward high-quality solutions, demonstrating superior potential for reliable social simulation. Source codes and datasets are publicly released at: https://github.com/WUT-IDEA/BEACOF.

Paper Structure

This paper contains 30 sections, 1 theorem, 6 equations, 4 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Cooperative Multi-Agent Collaboration
  4. Competitive Multi-Agent Collaboration
  5. Game-Theoretic Approaches to Multi-Agent Collaboration
  6. Dynamic Game Formulation
  7. Methodology
  8. Overview
  9. Approximate Perfect Bayesian Equilibrium
  10. Approximate Sequential Rationality
  11. Belief Update with Confidence Decay
  12. Theoretical Analysis: Beliefs Convergence
  13. Experiments
  14. Experimental Setup
  15. Implementation Details
  16. ...and 15 more sections

Key Result

proposition 1

Let the belief update follow Eq. eq:belief_update with $\lambda \in (0,1)$, assuming the meta-agent's evaluation $e_t$ is an unbiased estimator of the true capability with bounded variance $\sigma^2$. As $t \to \infty$, the belief dynamics exhibit Effective Memory Stabilization, where the accumulate

Figures (4)

  • Figure 1: Comparison of three collaboration types in a judicial deliberation task.
  • Figure 2: Overview of the Belief-driven Adaptive Collaboration Framework (BEACOF). The framework models collaboration as a dynamic game of incomplete information, applicable across diverse scenarios with specific belief dimensions (top panel). The central workflow executes as follows at round $t$: (1) Meta-Agent Coordination: The centralized Meta-Agent utilizes scenario history to generate contextual payoffs $U_t$ and predict probability distributions over agent collaboration types. (2) Agent Strategic Action: A Participant Agent $i$, conditioned on its private profile and the Meta-Agent's outputs, computes an approximate best response strategy $c_i^*$ and generates an interaction message $m_i^*$. (3) Evaluation & Belief Update: The Meta-Agent evaluates $m_i^*$ to produce a capability estimate tuple $(e_i^t, \omega_i^t)$. The dashed callout box on the right details the critical Gaussian belief update mechanism: other peers (e.g., Agent $j$, bottom left) refine their prior belief estimates regarding agent $i$, denoted as $\mathbf{b}_j^{t-1}(i)$, by integrating this new evidence $e_i^t$ weighted by confidence scores and a forgetting factor $\lambda$. This cyclic process drives the evolution of beliefs and strategic adaptation.
  • Figure 3: Ablation study (Llama3.1-8B-Instruct): removing belief updates or fixing collaboration type degrades performance across scenarios.
  • Figure 4: The case study of dynamic collaboration type switching in resolving complex medical reasoning tasks. The framework BEACOF adaptively shifts the interaction type, guiding agents from an initial incorrect consensus to the ground truth.

Theorems & Definitions (1)

  • proposition 1: Bounded Convergence of Belief Estimates