It is now well known that in order to solve global environmental problems, such as global warming, a volunteer participation of sovereign countries to international environmental agreements is needed. However, the effects of greenhouse gases on global warming are not completely known; for instance, there is a lot of uncertainty about the impact of accumulated pollution on the global temperature. In this paper we consider a situation in which countries do not fully know the magnitude of the consequences caused by the accumulation of greenhouse gases. Countries are however able to increase their knowledge by using a Bayesian learning process, on the basis of their observation of the actual damages they incur. Moreover, we assume that some countries are engaged in an agreement aimed at reducing pollution emissions, while others are not. We study the consequences of uncertainty and learning in terms of pollution emissions and welfare, for both signatory and non-signatory countries.