We study an extension of the Gale--Shapley marriage model and the Shapley--Shubik assignment model by considering linear valuations and bounded side payments. Our model includes the Eriksson--Karlander hybrid model as a special case. We propose a polynomial-time algorithm which finds a pairwise-stable outcome.
"A Polynomial-Time Algorithm for a Stable Matching Problem with Linear Valuations and Bounded Side Payments." Japan J. Indust. Appl. Math. 25 (1) 83 - 98, February 2008.