The linking of emission permit markets allows participants in different systems to purchase allowances from each other for the purpose of domestic compliance. A recent paper studied the efficiency gains generated in multilateral linkings between permit markets, and concluded that, despite the linking of all jurisdictions maximizing gains, it is not likely to emerge as it is not the most preferred option by all participants. We formulate the linking problem as a cooperative game and show that the linking of all jurisdictions satisfies core stability criteria. Thus, no subset of jurisdictions would benefit from creating their separate market, and the gains will be maximized. We then extend our analysis to arbitrary partitions and farsightedness level and analyze the stable linking of markets between Australia, Canada, the EU, South Korea, and the U.S. Our results indicate that the most likely stable configuration includes a market that links Australia, the EU, and the U.S., and another in which Canada is linked with South Korea. This scenario leaves about 15% of the potential gains unrealized. To mitigate this issue, we suggest that efficiency gains from market linkage be allocated according to the Shapley value, in which case our results suggest that we would see stable linking of all five jurisdictions and thus increase the efficiency.