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 thewell-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.