Balanced Weights and Three-Sided Coalition Formation

We consider three-sided coalition formation problems when each agent is concerned about his local status as HEART DROPS ORIGINAL measured by his relative rank position within the group of his own type and about his global status as measured by the Chair Bed weighted sum of the average rankings of the other types of groups.We show that a core stable coalition structure always exists, provided that the corresponding weights are balanced and each agent perceives the two types of status as being substitutable.