BEACOF: Belief-Driven Multi-Agent Collaboration

Official implementation for the paper: > Belief-Driven Multi-Agent Collaboration via Approximate Perfect Bayesian Equilibrium for Social Simulation > Weiwei Fang, Lin Li, Kaize Shi, Yu Yang, and Jianwei Zhang > The Web Conference (WWW) 2026

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📖 Overview

High-fidelity social simulation demands agents capable of authentically replicating the dynamic spectrum of human interaction. Current Multi-Agent Systems (MAS) often adhere to static interaction topologies, leading to "groupthink" (in pure cooperation) or deadlocks (in pure competition).

BEACOF (Belief-Driven Adaptive Collaboration Framework) is a novel framework that models social interaction as a dynamic game of incomplete information. Inspired by Approximate Perfect Bayesian Equilibrium (PBE), BEACOF enables agents to:

1. Maintain Beliefs: Iteratively refine probabilistic beliefs about peer capabilities based on interaction history.
2. Adaptive Strategy: Autonomously switch between Cooperation, Competition, and Coopetition (collaborative competition).
3. Ensure Rationality: Make sequentially rational decisions under uncertainty without needing full information.

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🚀 Key Features

• Dynamic Strategy Switching: Agents are not fixed to a single role; they transition dynamically between cooperative knowledge synthesis and competitive critical reasoning.
• Gaussian Belief Updates: Implements a tractable parametric Bayesian update mechanism with a forgetting factor to track non-stationary peer capabilities.
• Meta-Agent Coordination: A centralized coordinator estimates contextual payoffs and evaluates message quality to drive belief evolution.
• Multi-Scenario Generalization: Validated across three distinct social interaction archetypes:
  • ⚖️ Adversarial: Judicial/Court Debate.
  • 🏥 Mixed: Medical Q&A (MedQA).
  • 🗣️ Open-Ended: Persona-based Social Chat.

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🛠️ Installation

Prerequisites

• Python 3.9+
• Ollama (for local LLM inference as described in the paper)

Setup

1. Clone the repository

   git clone [https://github.com/WUT-IDEA/BEACOF.git](https://github.com/WUT-IDEA/BEACOF.git)
   cd BEACOF
   

2. Install dependencies

   pip install -r requirements.txt
   

3. Model Setup (Ollama) Ensure you have the backbone models pulled via Ollama. We utilize the following models in our experiments:

   ollama pull llama3.1
   ollama pull gemma2:9b  # (Check specific tag for Gemma3 equivalent)
   ollama pull qwen2.5:32b # (Check specific tag for Qwen3 equivalent)
   

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📂 Project Structure

BEACOF/
├── data/
├── src/
│   ├── AgentsCourt/
│   ├── mechanism/
│   └── prompts/
│	├── interaction.py                 # Entry point for simulations
│	└── ollama.py
└── README.md

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🏃 Usage

You can run simulations for different scenarios using main.py.

Start Simulation

# 1. Court Debate Simulation
python main.py court

# 2. Medical Consultation Simulation
python main.py medqa

# 3. Daily Chat Simulation
python main.py persona

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🧩 Methodology Highlights

The Loop

1. Payoff Generation: The Meta-Agent generates contextual payoffs $U_t$ based on interaction history.
2. Action Prediction: Probability distributions over collaboration types are predicted.
3. Strategic Action: Participant agents calculate an approximate Best Response ($c_i^*$) maximizing expected utility.
4. Belief Update: Agents update Gaussian beliefs about peers using the evaluation $e_j^t$ and confidence $\omega$, modulated by a forgetting factor $\lambda$.

Equation: Belief Update

$b_{i}^{t}(j) = \frac{\omega_{i}^{t-1}(j) \cdot b_{i}^{t-1}(j) + \omega_{j}^{t} \cdot e_{j}^{t}}{\omega_{i}^{t-1}(j) + \omega_{j}^{t}}$

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📝 Citation

If you find this code or our paper useful, please cite:

@inproceedings{fang2026beacof,
  title={Belief-Driven Multi-Agent Collaboration via Approximate Perfect Bayesian Equilibrium for Social Simulation},
  author={Fang, Weiwei and Li, Lin and Shi, Kaize and Yang, Yu and Zhang, Jianwei},
  booktitle={Proceedings of the ACM Web Conference 2026 (WWW '26)},
  year={2026},
  publisher={ACM},
  address={Dubai, United Arab Emirates}
}

📧 Contact

For any questions, please contact:

• Weiwei Fang: 311137@whut.edu.cn
• Lin Li: cathylilin@whut.edu.cn