At COP21, about 160 countries proposed the so-called INDCs that define GHG abatement objectives by 2030. While encouraging, these commitments are not ambitious enough to achieve the 2°C threshold by 2100, and further negotiations are needed for sharing the burden among countries. In this paper, we use a game theoretic approach for the design of fair agreements concerning additional abatements. In this game model, one defines a global extra emission budget up to 2050 that is compatible with the given temperature increase target by 2100. This global budget is a coupled constraint for all the countries when they define their climate policies. Therefore, this global budget will have to be distributed among countries, and the negotiation should be centered on this distribution, which should lead to a fair sharing of welfare losses. A non-cooperative dynamic game simulates countries’ policies, in which the strategies define the supply of emission permits, assuming that an international carbon market with full banking and borrowing is put in place. The resulting welfare losses take into account abatement costs and net costs/revenues from permit trading. The game is thus used for evaluating the economic consequences of INDCs, as well as for defining budget allocations that balance welfare losses equitably among countries. We show that fair climate agreements compatible with the 2°C target may be achieved at the moderate global cost of 0.8% of discounted total household consumption. Assuming an efficient international market and participation of all countries in the game provides a benchmark for what could be achievable in coming negotiations.