  We study a cooperative game setting where the grand coalition may change
since the initial players can invite more players. We focus on monotone games,
i.e., adding more players to the grand coalition is not harmful. We model the
invitation relationship as a directed acyclic graph. Our goal is to design a
reward distribution mechanism for this new cooperative game setting such that
players are incentivized to invite new players. In this paper, we propose the
weighted permission Shapley value (inspired by permission structure and the
weighted Shapley value) to achieve the goal. Our solution offers the very first
attempt to incentivize players to invite more players to form a larger
coalition via their private invitations in cooperative settings.
