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

Abstract

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.