Incentives to Invite Others to Form Larger Coalitions

We study a cooperative game setting where players form a network and each player only knows the existence of the players to whom she connects. Initially, only a subset of the players are in the game. Our goal is to design a reward distribution mechanism to incentivize the players to use their connections to invite more players to join the game. We show that the existing solutions such as the Shapley value cannot achieve this. Hence, to combat this problem, we propose a solution called weighted permission Shapley value (inspired by permission structure and the weighted Shapley value). Under this solution, for each player, inviting all her neighbors is a dominant strategy in all monotone games. We further prove that the solution is unique for tree networks. Our solution offers the very first attempt to incentivize the players to invite others to form a larger coalition in cooperative games.