Matching

Consider the following problem. Some individuals in a society are X’s and others are Y ’s. Every individual of each type has to be matched with one and only one individual of the other type. For example, managers have to be matched with assistants, or pilots have to be matched with copilots. Each X has preferences over the Y ’s and each Y has preferences over the X’s. Every individual prefers to be matched than to remain unmatched. We look for matching methods that result in sensible outcomes given any preferences.