BeliefNest: A Joint Action Simulator for Embodied Agents with Theory of Mind

TL;DR

BeliefNest addresses the need for explicit nested beliefs in embodied agents by introducing a Minecraft-based, open-source simulator that maintains hierarchically nested belief simulators for each agent and provides prompt-generation support to drive LLM-based control. It enables mental simulations within each agent's belief stack by constructing a real-world simulator alongside belief simulators and using path-based nesting with $Z$ and $Z||i$ to encode belief levels. The authors validate the framework with Sally-Anne and Ice Cream Van tasks, showing that agents can infer others' beliefs and predict belief-based actions, including second- and third-order reasoning, when guided by LLMs. This work offers a flexible platform with timeline branching for exploring joint-action strategies and invites integration with LLMs to advance ToM-enabled collaboration in robotics and dialogue systems.

Abstract

This paper introduces an open-source simulator, BeliefNest, designed to enable embodied agents to perform collaborative tasks by leveraging Theory of Mind. BeliefNest dynamically and hierarchically constructs simulators within a Minecraft environment, allowing agents to explicitly represent nested belief states about themselves and others. This enables agent control in open-domain tasks that require Theory of Mind reasoning. The simulator provides a prompt generation mechanism based on each belief state, facilitating the design and evaluation of methods for agent control utilizing large language models (LLMs). We demonstrate through experiments that agents can infer others' beliefs and predict their belief-based actions in false-belief tasks.

Figures (4)

• Figure 1: Overview of BeliefNest. The nested belief structure derived from Theory of Mind is implemented using multiple physical simulators. Each agent can perform mental simulations within its own simulator, considering the beliefs of others, to generate action plans that reflect these beliefs.
• Figure 2: Overall structure of BeliefNest. The simulators form a nested hierarchy that corresponds to the nested structure of beliefs. Let $Z$ be a finite sequence of agent identifiers that represents a path of belief nesting. In the simulator representing state $s^{Z}$, agent $i$ constructs a new simulator whose state $s^{Z||i}$ reflects its belief $b^Z_i$. Here, the operator $||$ denotes sequence concatenation: $Z||i$ is the sequence obtained by appending agent $i$ to the end of $Z$. In the real world, agent 1 can see the red and green blocks, while agent 2 can see the blue and green blocks. Agent 1 is unaware of the blue block, and agent 2 is unaware of the red block. Therefore, agent 1 believes that agent 2 can see only the green block. These belief-dependent perceptions are explicitly represented within each simulator. All agents are assumed to have prior knowledge of the floor, the white outer walls, and the black inner wall.
• Figure 3: Experimental setup for the Sally-Anne task. Sally's position in the figure represents her location after placing the diamond in the box.
• Figure 4: Experimental setup for the Ice Cream Van Task.