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The game theory perspective provides insights into the strategic decision-making processes of the governments regarding the problem of climate change. We propose a model of strategic interactions among countries in which each government is concerned with its own benefit, as well as with the benefits of all the other countries.The model is a vector-valued non-cooperative game that permits the representation of situations in which the preferences of the governments are incomplete and there is imprecision about the degrees of altruism. The focus is on the identification of the potential equilibria that will eventually be reached when the governments show different attitudes towards other countries or groups of countries. 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