A Computable Game-Theoretic Framework for Multi-Agent Theory of Mind
Fengming Zhu, Yuxin Pan, Xiaomeng Zhu, Fangzhen Lin
TL;DR
The paper addresses creating a computational Theory of Mind for multi-agent systems using a game-theoretic lens. It introduces a stochastic game framework and a Gamma-Poisson cognitive hierarchy to model beliefs about others' reasoning levels, enabling recursive perspective-taking. To maintain tractability, it provides two best-response constructions: solving induced MDPs and a QMDP approximation, together with Bayesian belief updates that yield a mixed strategy over levels. By connecting to I-POMDP while emphasizing computability, the framework aims to scale ToM reasoning to larger domains, with applications in robotics and AI and planned human–robot experiments.
Abstract
Originating in psychology, $\textit{Theory of Mind}$ (ToM) has attracted significant attention across multiple research communities, especially logic, economics, and robotics. Most psychological work does not aim at formalizing those central concepts, namely $\textit{goals}$, $\textit{intentions}$, and $\textit{beliefs}$, to automate a ToM-based computational process, which, by contrast, has been extensively studied by logicians. In this paper, we offer a different perspective by proposing a computational framework viewed through the lens of game theory. On the one hand, the framework prescribes how to make boudedly rational decisions while maintaining a theory of mind about others (and recursively, each of the others holding a theory of mind about the rest); on the other hand, it employs statistical techniques and approximate solutions to retain computability of the inherent computational problem.