Apr. 10 (10:00-11:00) room C.510
Mánuel Mágó (Corvinus)
The participation surplus value, equal division, and a family containing both
We consider cooperative transferable utility games. We define a new solution concept, called the participation surplus value, that assigns to every player the sum of their per capita net participation surplus, i.e. the difference between the value of a given coalition they are in and its complement. We give an axiomatic characterization of the participation surplus value. The axioms are based on the well-known set of four axioms used to characterize the Shapley value. We use the familiar linearity, symmetry, and efficiency axioms, and complete the set with a new axiom called complete contribution retention. Complete contribution retention is satisfied whenever only the worth of a single coalition changes, the sum of the values assigned to its members are changing in the exact same way. We show that the axioms are independent. We show that for games with two or three players, the participation surplus value is a linear combination of the Shapley value and equal division of the worth of the grand coalition. We also show that for any game the participation surplus value can be written as a linear combination of Banzhaf values, expanded for coalitions. When contribution retention is set to the other extreme, the resulting zero contribution retention axiom, together with linearity, symmetry, and efficiency, is used to characterize the equal division of the worth of the grand coalition. When contribution retention is allowed to be partial, or even more than one or less than zero, we define a family of concepts, its members being the linear combination of equal division and the participation surplus value. Linearity, symmetry, efficiency, and partial contribution retention characterize any member of the family.
The talk is based on joint work with Adél Luca Szűcs.