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Inter-domain peering links represent nowadays the real bottleneck of the Internet. On peering links carriers may coordinate to efficiently balance the load, but the current practice is often based on an uncoordinated selfish routing supported by the peer relationship. We present a novel game theoretical routing framework to efficiently coordinate the routing on peering links while modelling the non-cooperative carrier behaviour. It relies on a collaborative use of the multi-exit discriminator (MED) attribute of BGP, hence it is nicknamed ClubMED (coordinated MED). The incentives are the minimization of carrier routing costs, the control of peering link congestions and peering route stability. For the ClubMED game, we define the Nash equilibrium multi-path (NEMP) routing policy that shall be implemented upon Nash equilibria and Pareto-efficient profiles. Intra-domain interior gateway protocol (IGP) weight optimizations are consistently integrated into the framework. We emulated the peering settlement between the Internet2 and the Geant2 networks, employing real datasets, comparing the ClubMED results to the current BGP practice. The results show that the global routing cost can be reduced of roughly 17%, that the peering link congestion can be avoided and that the stability of the routes can significantly be reinforced.