Understanding how cooperation emerges and persists is a central challenge in evolutionary game theory. Existing models often rely on restricted, hand-picked strategy sets, which can overlook critical behavioural pathways. A recent four-strategy framework showed that cheap talk can promote cooperation through local interactions, yet it remained unclear whether modelled strategies might alter these conclusions. Here, we extend this framework to the complete set of eight strategies that naturally arise from communication and decision-making rules. We show that incorporating the full strategy space dramatically changes the evolutionary landscape. Cooperation becomes both more robust and more versatile, driven by novel pathways absent in the restricted model. In particular, we uncover a previously overlooked mechanism in which suspicious cooperation catalyses a cyclic dynamic that sustains cooperation. Conversely, the assumed role of strategic defection in the biased model is fragile, acting mainly as a spoiler rather than a genuine evolutionary attractor. The complete model further reveals a rich spectrum of long-term behaviours, including 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 and highlight the importance of comprehensive modelling when explaining the emergence of cooperation.

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