Sharing the Surplus and Proportional Values

Abstract

We introduce a family of proportional surplus division values for TU-games. Each value first assigns to each player a compromise between his stand-alone worth and the average stand-alone worths over all players, and then allocates the remaining worth among the players in proportion to their stand-alone worths. This family contains the proportional division value and the new egalitarian proportional surplus division value as two special cases. We provide characterizations for this family of values, as well as for each single value in this family.

Equal Loss under Separatorization and Egalitarian Values

“…Given a TU-game, separatorization (Zou et al, 2020) of a player means that the worth of any coalition containing this player becomes equal to the sum of the stand-alone worths of the players in this coalition.…”