Large language models (LLMs) are increasingly deployed as autonomous agents that negotiate, coordinate, and make decisions on behalf of human users. Understanding how they cooperate is therefore important for AI governance and machine behaviour research. We examine two factors: payoff magnitude and interaction language. Classical game theory predicts that multiplying all payoffs by a positive constant should not change behaviour because the underlying strategic incentives remain unchanged. We test this prediction using five widely adopted commercial LLMs playing an iterated prisoner's dilemma across ten payoff scales and five languages (English, French, Vietnamese, Chinese and Arabic). Contrary to theoretical expectations, changing only the numerical scale of payoffs substantially alters cooperation. Models respond differently, often in opposite directions, meaning that averages across models can conceal important behavioural heterogeneity. Sensitivity to payoff scale also depends strongly on prompt language. Moreover, payoff scale modifies the effects of persona instructions: at sub-unit stakes, where no payoff shown exceeds 1, all five models cooperate more under a selfish than a cooperative persona, whereas Claude and Gemini reverse this pattern at larger scales. These findings show that cooperation measures depend critically on payoff scale and language and should not be treated as fixed model traits.

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