The supplier–firm–buyer game and its m-sided generalization

Abstract Two-sided assignment games are a natural model for buyer–seller markets. The focus on the firm in business strategy suggests the use of a three-sided game to model suppliers, firms, and buyers. Although, in general, a three-sided game may have an empty core, this paper shows that the supplier–firm–buyer game of Brandenburger and Stuart (1996) always has a non-empty core. This class of games suggests a condition, called local additivity, which is shown to be a sufficient condition for non-emptiness of the core in m -sided assignment games.