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In the framework of international cooperation on climate change to control greenhouse gas emissions
(GHG), this paper aims to shed new light on the eventuality of the emergence of a country (or a group
of countries) behaving as a leader in the implementation of its environmental policy. The sequence of
moves in the existing literature is usually an exogenous assumption, – known as the Cournot
assumption (if countries take action simultaneously) and the Stackelberg assumption (if they act
sequentially, the latter observing the strategy of the former). The main purpose here is to make the
timing endogenous. To do so, we introduce a pre-play stage in the basic two-country game. Then we
provide different sets of minimal conditions – on the benefit and damage functions linked to GHG
emissions into the atmosphere, yielding respectively the simultaneous and the two sequential modes of
play. While the results essentially confirm the prevalence of the former, they also indicate that the
latter are natural under some robust conditions: a leader can emerge endogenously when
implementing its environmental policy. Finally we provide sufficient conditions for a specific leader
to appear. All the results come with an analysis in terms of global emissions and global welfare. No
extraneous assumptions such as concavity, existence, or uniqueness of equilibria are needed, and the
analysis makes crucial use of the basic results from the theory of supermodular games.