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We considered a humanitarian environment composed of donors and non-governmental organizations (NGOs) that the non-profits may adopt competitive or coopetitive inter-organizational interaction for managing the disasters. We also assumed that the government intervenes in the relief operations by applying one of its two policies; social welfare maximization (SWM) or budget consumption minimization (BCM). Using game theory (GT) approach, we develop 4 scenarios and, as a result, 4 mathematical programming models for examining the effect of the NGOs interactions and the government policies on the performance of donors, NGOs and government. We find that coopetition of NGOs facilitates the achievement of the government's objectives, and it also helps the non-profits to become more successful in providing relief. The government prefers to provide the indirect relief to the nonprofits to manage emergency operations successfully, and the financial aids are given only in the condition of reducing the level of NGOs cooperation. We also conclude that the cooperation of NGOs increases the donors' utility. A numerical example is conducted to test the findings of the models. • Cooperation and competition models are developed for humanitarian SCs interaction. • Leader-follower game model is established for interactions of the SCs and government. • Welfare maximization or budget consumption minimization are the government's policies. • The government prefers to give financial aids rather than reliefs to the NGOs. • Cooperation among NGOs in relief operations is beneficial for government and donors. [ABSTRACT FROM AUTHOR]