Matching with partially ordered contracts
In this paper, we study a many-to-many matching model with contracts. We extend the economic model of Hatfield and Milgrom by allowing a partial order on the possible bilateral contracts of the agents in a two-sided market economy. To prove that a generalized stable allocation exists, we use generalized form of properties like path-independence and substitutability. The key to our results is the well-known lattice theoretical fixed point theorem of Tarski. The constructive proof of this fixed point theorem for finite sets turns out to be the appropriate generalization of the Gale–Shapley algorithm also in our general setting.