In this paper we define and solve a ‘robust game design’ problem that could be used to assess the fair sharing of the abatement burden among the 28 EU countries in their coming climate negotiations. The problem consists in finding a distribution of a global ‘safety emission budget’ for the panning period 2010–2050, among the 28 countries in such a way to obtain a balanced relative loss of welfare (computed in percent of the discounted consumption in the reference case) when the countries supply strategically their permit endowment on a permit trading system with full banking and borrowing. We assume that the countries play a noncooperative game, where the payoffs are constituted of the gains from the terms of trade plus the gains in the permit trading and minus the abatement cost, expressed as the compensative variation of income. These payoff functions are estimated from an ensemble of numerical simulations of a detailed CGE model, GEMINI-E3 representing the economic interactions among the 28 EU countries. To deal with the uncertainty introduced by the statistical emulation technique we propose to use the concept of robust equilibrium, where the results of robust optimization are exploited in the definition of an equilibrium solution, when the payoff is subject to uncertainties. A numerical illustration is performed and an interpretation of the impact of the robustification approach on the solution of the game design problem is provided.