In this paper we propose a non-cooperative meta-game approach to designing and assessing climate agreements among 28 European countries that will be compatible with the EU 2050 climate target. Our proposed game model is identified through statistical emulation of a large set of numerical simulations performed with the computable general equilibrium model GEMINI-E3. In this game, the players are the 28 European countries, the payoffs are related to welfare losses due to abatements and the strategies correspond to the supply of emission rights on the European carbon market. We show it is possible to design a fair burden-sharing rule that equalizes welfare losses between countries to approximately 1.2 % of their discounted household consumption. The associated European CO2 price in 2050 reaches $1100, a figure in line with previous studies. Lastly, the paper discusses various implementation issues of these types of negotiations and evaluates the cost of non-cooperation among EU countries.