Contractual $M$-core and equilibrium allocations

The paper deals with equilibrium characterization of the so-called totally contractual allocations [1–3]. As a consequence of the characterization obtained, a rather strong coalitional stability of equilibrium allocations is established. Due to the complicated logical structure of contractual blocking, we pay strong attention to the pure descriptive aspects of the concepts under consideration. Quite simple sufficient conditions guaranteeing coincidence of the totally contractual core and the set of Walrasian equilibrium allocations are established, and the structure of domination relations induced by several rules of breaking the contracts is studied. Game-theoretic approach elaborated in the paper rests on reduction of the original blocking to some more simple domination relations in cooperative games, associated with the contractual blocking in question.