  In this paper we introduce the $\Gamma$ value, a new value for cooperative
games with transferable utility. We also provide an axiomatic characterization
of the $\Gamma$ value based on a property concerning the so-called necessary
players. A necessary players of a game is one without which the characteristic
function is zero. We illustrate the performance of the $\Gamma$ value in a
particular cost allocation problem that arises when the owners of the
apartments in a building plan to install an elevator and share its installation
cost; in the resulting example we compare the proposals of the $\Gamma$ value,
the equal division value and the Shapley value in two different scenarios. In
addition, we propose an extension of the $\Gamma$ value for cooperative games
with transferable utility and with a coalition structure. Finally, we provide
axiomatic characterizations of the coalitional $\Gamma$ value and of the Owen
and Banzhaf-Owen values using alternative properties concerning necessary
players.
