Exact stability and its applications to strong solvability

We introduce the exact core and the biexact core of a strategic game form. Those are solutions which lie between the usual b-core and the set of strong equilibrium outcomes. We define the corresponding notion of exact and biexact stability. We prove that a game form is exactly stable if and only if it is exact, tight and subadditive and that it is biexactly stable if and only if in addition it is biexact. As an application, we study the exactness of rectangular game forms. We prove that an exact rectangular game form is essentially a one-player game form. In particular any strongly solvable rectangular game form is essentially a one-player game form. This generalizes a result of Ichiishi, 1985.  2000 Elsevier Science B.V. All rights reserved.