  In this paper, we study the egalitarian solution for games with discrete side
payment, where the characteristic function is integer-valued and payoffs of
players are integral vectors. The egalitarian solution, introduced by Dutta and
Ray in 1989, is a solution concept for transferable utility cooperative games
in characteristic form, which combines commitment for egalitarianism and
promotion of indivisual interests in a consistent manner. We first point out
that the nice properties of the egalitarian solution (in the continuous case)
do not extend to games with discrete side payment. Then we show that the Lorenz
stable set, which may be regarded a variant of the egalitarian solution, has
nice properties such as the Davis and Maschler reduced game property and the
converse reduced game property. For the proofs we utilize recent results in
discrete convex analysis on decreasing minimization on an M-convex set
investigated by Frank and Murota.
