LLMs agents are increasingly used in multi-agent settings, yet their behaviour in sustainability games remains largely unexplored. This work investigates whether lying can emerge among LLM agents in a competitive sustainability game in which agents are informed that common resources can regenerate, although regeneration does not actually occur. We develop an agent-based model of a sustainability game in which agents manage industrial, military, and ecological resources, and interact through a network. LLM agents can observe neighbours' status, declare future attacks, receive permission to lie, and access reputation information, while rule-based agents provide an interpretable behavioural baseline. The results show that neighbour information strongly changes system dynamics, increasing attacks while improving biosphere retention and coexistence. Also, the presence of future declarations reduce extinction risk without suppressing conflict. Behaviourally, deception emerges even when agents are not explicitly allowed to lie, and explicit permission mainly increases bluffing and diversion rather than direct backstabbing. Finally, the presence of reputation memory and information about the current biosphere level reduces system ecological depletion. These findings suggest that deception can arise as an emergent behaviour in LLM-agent systems and that communication between LLM-agents could support sustainability while dealing with risk.

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