Linear-efficient-symmetric values and inequality in TU-games

Abstract This paper introduces a dominance criterion that determines whether a TU-game is less unequal than another. A game is derived from another by non-void sequences of inequality-reducing transfers of worth between coalitions of equal size if and only if the resulting game is less unequal in the Lorenz sense. The paper also measures payoff inequality among players (for a TU-game) through the Lorenz criterion. When a distribution (allocation) of payoff is issued from another by non-void sequences of inequality-reducing transfers of payoff between players, the resulting distribution of payoff is less unequal according to the Lorenz criterion (and conversely). It is shown that any linear-efficient-symmetric value, being invariant and separable under worth transfers and satisfying a fair treatment axiom, converts an inequality-reduction in TU-games into a decrease in payoff inequality among players.