This paper deals with an application of the robust equilibrium concept in game theory to the assessment of the possible international agreement on climate that could be achieved in the conference of the parties negotiations organized by the UNFCCC. It is shown in particular that an acceptable, self-enforcing agreement could be obtained to maintain the temperature rise below 2 ∘ C at the end of twenty-first century, with a balanced welfare loss among 11 groups of countries representing the parties limited to 1.8 % of their total discounted household consumption. To design this possible agreement we use a reduced order meta game where the players are the 11 groups of countries considered as the parties in negotiation, the strategies are the supply of emission quotas on an international emissions trading system and the payoffs are the net gains obtained from the emissions, trading and changes in the terms of trade minus the damage cost associated with the cumulative emissions during the 2010–2050 period. To identify the abatement costs that serve in the calculation of the payoffs and the gains due changes of terms of trade we use a statistical emulation of the GEMINI-E3 macroeconomic model. To obtain surrogate damage cost functions we introduce a coupled constraint in the game, imposing a limit to the cumulative emissions of all parties, which we call the global safety emissions budget. The multipliers intervening in the equilibrium necessary conditions are then interpreted as marginal damage costs. Games with coupled constraints admit a manifold of normalized equilibria and we show that they correspond to equilibria in games where each player is constrained by a given share of the safety emissions budget. Among all the normalized equilibria we look for the one which minimizes the maximum welfare loss, expressed in percentage of household consumption, among the 11 groups of countries. To take into account the uncertainty created by the statistical emulation approach and the approximate description of the emissions trading system we introduce robustness in the equilibrium computation.