The Conference of Parties (COP) aims to address the global warming problem through agreements for reducing emissions. However, the current strategies fall short due to minimal efforts for emission reductions driven by short-term economic considerations. To better understand under which circumstances countries may have more virtuous behavior, we propose a static game model. In this model, the players are represented by governments, and their actions correspond to emissions levels. The utilities are a trade-off between economic benefits and damage caused by climate change. A key feature of the game is that it is parameterized by a state, which is precisely the state of the climate dynamics. We conduct the Nash equilibrium analysis. In the numerical analysis, we assess the impact of the damage function on the behavior of the governments.