An axiomatization of the egalitarian solutions
This paper considers the axiomatic solution of cooperative games without transferable utility with the egalitarian solution of E. Kalai and the author. Let S be a coalition and V(S), the utilities S can achieve. Let N be the grand coalition. Denote by \(G_ 0\) the class of games such that V(S) is closed, convex, and comprehensive for each S. Denote by \(G_ 1\) the class of games in \(G_ 0\) such that V(N) is smooth and not level. The main results are as follows. There is no solution function on \(G_ 0\) satisfying scale covariance, conditional additivity, independence of irrelevant alternatives, and unanimity. The importance of this is that both the NTU value and the Harsanyi solution satisfy these conditions on \(G_ 1\). However, there is a unique solution satisfying the above conditions (without scale invariance) and the following zero condition: if zero is on the boundary of V(S) for every S, then zero is a solution. This is the symmetric egalitarian solution on \(G_ 1\). If one asymmetrizes the unanimity condition, one has the nonsymmetric egalitarian solution.
scientific article; zbMATH DE number 3910177