Bayesian theory of mind promotes cooperation in spatial prisoner’s dilemma games

Understanding how cooperation emerges among self-interested individuals is a central problem in social sciences and artificial intelligence, especially in networked evolutionary games where interaction structure shapes collective outcomes. However, most spatial game models treat agents as behavior-based automata, lacking the ability to infer others’ intentions or latent mental states, which makes cooperation fragile under noise and strategic uncertainty. To address this limitation, we introduce agents endowed with Bayesian theory-of-mind (ToM) inference, enabling them to update beliefs about neighbors’ types and adapt their altruistic behavior accordingly. We study this framework across four canonical network topologies — square lattices, Erdős–Rényi random graphs, Watts–Strogatz small-world networks, and Barabási–Albert scale-free networks — using Monte Carlo simulations. We show that ToM mechanisms significantly expand the parameter region supporting cooperation, sustaining it even under high temptation to defect and inducing clear phase transitions. This advantage holds universally across all network structures considered. At the microscopic level, Bayesian learning exhibits a pronounced asymmetry: defection is detected rapidly, whereas cooperative ties form gradually. These results highlight the critical role of cognitive inference in reshaping cooperation and establish a unified framework linking theory-of-mind reasoning with networked evolutionary games.