Buyer–seller exactness in the assignment game

In the assignment game framework, we try to identify those assignment matrices in which no entry can be increased without changing the core of the game. These games will be called buyer–seller exact games and satisfy the condition that each mixed-pair coalition attains the corresponding matrix entry in the core of the game. For a given assignment games, a unique buyer–seller exact assignment game with the same core is proved to exist. In order to identify this matrix and to provide a characterization of those assignment games which are buyer–seller exact in terms of the assignment matrix, attainable upper and lower core bounds for the mixed-pair coalitions are found. As a consequence, an open question posed in Quint regarding a canonical representation of a “45°-lattice” by means of the core of an assignment game can now be answered.