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The Paris Agreement relies on nationally determined contributions to reach its targets and asks countries to increase ambitions over time, leaving open the details of this process. Although overcoming countries' myopic 'free-riding' incentives requires cooperation, the global public good character of mitigation makes forming coalitions difficult. To cooperate, countries may link their carbon markets(1), but is this option beneficial(2)? Some countries might not participate, not agree to lower caps, or not comply to agreements. While non-compliance might be deterred(3), countries can hope that if they don't participate, others might still form a coalition. When considering only one coalition whose members can leave freely, the literature following the publication of refs(4,5) finds meagre prospects for effective collaboration(6). Countries also face incentives to increase emissions when linking their markets without a cap agreement(7,8). Here, we analyse the dynamics of market linkage using a game-theoretic model of far-sighted coalition formation. In contrast to non-dynamic models and dynamic models without far-sightedness(9,10), in our model an efficient global coalition always forms eventually if players are sufficiently far-sighted or caps are coordinated immediately when markets are linked.