Linear criterion for testing the extremity of an exact game based on its finest min-representation

The paper also deals with different min-representations of a fixed exact game μ, which can be compared with the help of the concept of a tightness structure (of a min-representation) introduced in the paper. The collection of tightness structures (of min-representations of μ) is shown to be a finite lattice with respect to a refinement relation. We give a method to obtain a min-representation with the finest tightness structure, which construction comes from the coarsest standard min-representation of μ given by the (complete) list of vertices of the core (polytope) of μ. The newly introduced criterion for exact extremity is based on the finest tightness structure.