Pollution Permit Sharing Games

We consider a pollution permit sharing problem in which a ?nite number of countries, each identi?ed by a unique technology that transforms the pollution permits into an output, share a given amount of permits. We de?ne a Pollution Permit Sharing (PPS) game that assigns to each coalition of countries the maximal value of output they can generate collectively with their technologies and permits available to them. We show that the game is totally balanced. We also show that, for the well-known Cap and Trade (CAT) mechanism, namely the competitive equilibrium allocation which generates an efficient allocation of the permits, its corresponding (net) output distribution is in the core of the PPS game. We consider two other coalitional games whose de?nitions depend on the availability of either the total permits or the technologies. The Aspiration Upper Bound with given Permits (AUBP) game assigns to each coalition the maximal value they can generate by using the technologies available from all countries, but only with the permits available to the coalition. And the Aspiration Upper Bound with given Technologies (AUBT) game assigns to each coalition the maximal value they can generate using only the technolo-gies available to the coalition with the permits available from all countries. We show that the core of the AUBP game is nonempty. More importantly, we show that the competitive equilibrium allocation violates the above two aspiration upper bound restrictions. Finally, we suggest the Shapley value as one of the possible alternative solutions to the permit sharing problem.