A two-sided discrete-concave market with possibly bounded side payments: An approach by discrete convex analysis

The marriage model due to Gale and Shapley (1962) and the assignment model due to Shapley and Shubik (1972) are standard in the theory of two–sided matching markets. We give a common generalization of these models by utilizing discrete–concave functions and considering possibly bounded side payments. We show the existence of a pairwise stable outcome in our model. Our present model is a further natural extension of the model examined in our earlier paper, and the proof of the existence of a pairwise stable outcome is even simpler than the previous one.