Many international treaties come into force only after a minimum number of countries have signed and ratified the treaty. Why do countries agree to introduce a minimum participation constraint among the rules characterising an international treaty? This question is particularly relevant in the case of environmental treaties dealing with global commons, where free-riding incentives are strong. Is a minimum participation rule a way to offset these free-riding incentives? Why do countries that know they have an incentive to free-ride accept to tie their hands through the introduction of a minimum participation constraint? This paper addresses the above questions by analysing a three-stage non-cooperative coalition formation game. In the first stage, countries set the minimum coalition size that is necessary for the treaty to come into force. In the second stage, countries decide whether to sign the treaty. In the third stage, the equilibrium values of the decision variables are set. At the equilibrium, both the minimum participation constraint and the number of signatories the coalition size are determined. This paper shows that a non-trivial partial coalition, sustained by a binding minimum participation constraint, forms at the equilibrium. This paper thus explains why in international negotiations all countries often agree on a minimum participation rule even when some of them do not intend to sign the treaty. The paper also analyses the optimal size of the minimum participation constraint.