We define a general fractional matching model. Each person has a set of potential partners and consumes a bundle of partnerships. Each person consumes the same quantity of a particular partnership as his partner does. Each person’s preferences are defined over partnership bundles.

This model has several natural applications: the assignment of probabil- ity distributions over deterministic matchings for marriage problems, school choice, scheduling workers at various work sites, organizing paired activities among a group, and so on.

For this novel model, we define a price based solution. We show that the core of each problem is non-empty. We show that our solution selects a subset of the core. We also show that if the number of people involved increases—in a way that there is a fixed number of “kinds” of people—the gains from misreporting preferences diminish.