The Nobel Prize in Economic Sciences 2012 and Matching Theory

Abstract

The Nobel Prize in Economic Sciences 2012 was awarded jointly to A. E. Roth and L. S. Shapley "for the theory of stable allocations and the practice of market design." The reason why it was awarded to A. E. Roth and L. S. Shapley is two-fold: their extremely valuable efforts in applying scientific findings in very important real life problems such as kidney exchange and student placement problems, and their contribution to the theory of stable matchings. In this talk, we will present the theory of stable matchings starting from the basics such as the Gale-Shapley Algorithm, discussing more advanced topics such as manipulation and existence of stable matchings under various conditions. Two important applications, namely kidney exchange and student placement problems will be given special consideration. In the second part of the talk, the role of graph theory in stable matchings will be discussed in more depth. In particular, the links between stable matchings and the problem of finding an inclusion-wise maximal matching of minimum size will be explored. As a natural consequence of this link, the need for studying various graph classes will be emphasized.