A Two-Sided Discrete-Concave Market with Bounded Side Payments: An Approach by Discrete Convex Analysis

The marriage model due to Gale and Shapley and the assignment model due to Shapley and Shubik 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 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 previous paper (Fujishige and Tamura [10]), and the proof of the existence of a pairwise stable outcome is even simpler than the previous one. Satoru Fujishige Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan. phone: +81-75-753-7250, facsimile: +81-75-753-7272 e-mail: [email protected]. Akihisa Tamura Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan. phone: +81-75-753-7236, facsimile: +81-75-753-7272 e-mail: [email protected].