Cohesive players: characterizations of a subclass of efficient, symmetric, and linear values

In this paper, we introduce the cohesive players and a related axiom called equal surplus of cohesive players. On this basis, we study the subclass of efficient, symmetric, and linear (ESL) values satisfying equal surplus of cohesive players. We first give an analytical formula and also propose two characterizations for this subclass of ESL values. With these characterizations, we discuss the relationships between this subclass and other classical ESL values, in particular the Shapley value. We then characterize each value in the subclass of ESL values satisfying equal surplus of cohesive players by introducing the $$\beta $$ β -null player surplus property and the $$\beta $$ β -reward cohesive player property. From this, we obtain new parallel characterizations of the Shapley value and the equal surplus division value. Moreover, we show that equal surplus of cohesive players can replace symmetry in many well-known characterizations of values.