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We study a cooperative game setting where the grand coalition may changesince 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 theinvitation relationship as a directed acyclic graph. Our goal is to design areward distribution mechanism for this new cooperative game setting such thatplayers are incentivized to invite new players. In this paper, we propose theweighted permission Shapley value (inspired by permission structure and theweighted Shapley value) to achieve the goal. Our solution offers the very firstattempt to incentivize players to invite more players to form a largercoalition via their private invitations in cooperative settings.

Incentives to Invite Others to Form Larger Coalitions