Existence of stable outcomes and the lattice property for a unified matching market

Abstract This paper establishes the existence of stable matchings, the lattice property of the core and the existence of optimal stable payoffs for each side of the market. We do this in a matching market consisting of a ‘mixed economy’ in which some firms compete by means of salary and others have no flexibility over terms of appointment. Common proofs are used, which unify the traditional discrete and continuous cases, namely the marriage and assignment models.