Zhao Song, Ndidi Bianca Ogbo, Xinyu Wang, Chen Shen, Matjaz Perc, The Anh Han
Understanding how cooperation emerges and persists is a central challenge in evolutionary game theory. However, models of communication often rely on restricted strategy sets, making it unclear whether omitted behaviours alter cooperation. Here, we study the complete deterministic eight-strategy space that naturally arises from the specified two-stage cheap-talk game. We show, both analytically and through agent-based simulations, that incorporating the full deterministic strategy space fundamentally changes the evolutionary landscape. In lattice populations, cooperation is sustained across wider parameter regions through previously overlooked cyclic dynamics involving suspicious cooperation, whereas strategic defection is fragile and mainly disrupts cooperation. The complete model also reveals stable coexistence among up to seven strategies and time-varying patterns of partial coexistence. These results demonstrate that the full strategy space unlocks hidden routes to cooperative behaviour, highlighting the importance of comprehensive modelling when explaining the emergence of cooperation. Cheap talk can encourage cooperation, but its success depends on which behaviours are allowed in the model. This study shows that considering the full deterministic strategy space reveals overlooked signalling behaviours that help cooperation persist on networks.