Deriving strong and coalition-proof nash equilibria from an abstract system

The notion of coalition-proof Nash equilibrium (CPNE) is derived from the (unique) von Neumann and Morgenstern (vN & M) abstract stable set of an abstract system. Furthermore, the abstract core of this same system yields the set of strong Nash equilibria (SNE). It follows that the two important solution concepts can be defined for games with any number of players. Furthermore, our results suggest that, at least intuitively, one can view the difference between SNE and CPNE as stemming from the negotiation process that is conducted; specifically, can credible counter threats be made?