Stackelberg Assumption vs. Nash Assumption in Partially Cooperative Games

We deal with n-person normal form games where a subset of players decide to cooperate (signatories) and choose strategies by maximizing the aggregate welfare of the coalition members as in International Environmental Agreements (IEA) context. The non-cooperating (non-signatories) players choose their strategies as a Nash equilibrium. In this paper the partial cooperative equilibrium (PCE) under the Nash-Cournot and the Stackelberg assumptions are considered and presented also in the case of non-signatories multiple decision. Some properties are discussed in both situations, particularly the profit of the players are compared.