  In cooperative games with transferable utilities, the Shapley value is an
extreme case of marginalism while the Equal Division rule is an extreme case of
egalitarianism. The Shapley value does not assign anything to the
non-productive players and the Equal Division rule does not concern itself to
the relative efficiency of the players in generating a resource. However, in
real life situations neither of them is a good fit for the fair distribution of
resources as the society is neither devoid of solidarity nor it can be
indifferent to rewarding the relatively more productive players. Thus a
trade-off between these two extreme cases has caught attention from many
researchers. In this paper, we obtain a new value for cooperative games with
transferable utilities that adopts egalitarianism in smaller coalitions on one
hand and on the other hand takes care of the players' marginal productivity in
sufficiently large coalitions. Our value is identical with the Shapley value on
one extreme and the Equal Division rule on the other extreme. We provide four
characterizations of the value using variants of standard axioms in the
literature. We have also developed a strategic implementation mechanism of our
value in sub-game perfect Nash equilibrium.
