Matching in Platform Markets

We model platform markets with the matching-with-contracts framework. The solution concept in matching with contracts, stability, has a natural interpretation in platform markets. We use this framework to explore properties in these markets including seesaw principle and market tipping. Finally, we consider an environment where agents who join the same platform need to have the same term. We show that substitutable preferences are not sufficient for the existence of a stable allocation, and that the existence is recovered when we impose an additional assumption that agents also have lexicographic preferences