A general two-sided matching market with discrete concave utility functions

In the theory of two-sided matching markets there are two standard models: (i) the marriage model due to Gale and Shapley and (ii) the assignment model due to Shapley and Shubik. Recently, Eriksson and Karlander introduced a hybrid model, which was further generalized by Sotomayor. In this paper, we propose a common generalization of these models by utilizing the framework of discrete convex analysis introduced by Murota, and verify the existence of a pairwise-stable outcome in our general model. 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]. † This work is supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan.