Ordinal equivalence of values, Pigou-Dalton transfers and inequality in TU-games

The paper examines the assessment of inequality in TU-games when individual payoffs are modeled using a notion of value. Especially, it studies inequality that affects the payoffs of Linear, Efficient and Symmetric values (LES values). We use the Pigou-Dalton transfers principle and the Lorenz criterion to compare LES values of weakly linear games (Freixas, 2010) and shed light on transfers of payoffs that may result from substituting a given LES value for another. We also characterize weak linearity in terms of Pigou-Dalton transfers. Since such transfers preserve the ordinal equivalence of values, the paper studies the ordinal equivalence of LES values in TU-games. Our study covers four classes of games which are ranked by set inclusion as follows: strongly linear games, linear games, sharply linear games and weakly linear games. We characterize the ordinal equivalence of LES values for each of these subclasses of TU-games.