Complements and substitutes in generalized multisided assignment economies

We consider a finitely populated economy in which there are different types of agent, each agent is of one type, and profit is created by coalitions containing at most one agent of each type. We present negative results establishing that agents of different type may not be complements and agents of the same type may not be substitutes. We propose novel notions for the complementarity and substitutability of disjoint coalitions, and we find conditions under which they hold.