A Model of Matching with Friction and Multiple Criteria

We present a model of matching based on two character measures. There are two classes of individual. Each individual observes a sequence of potential partners from the opposite class. One measure describes the ”attractiveness” of an individual. Preferences are common according to this measure: i.e. each individual prefers highly attractive partners and all individuals of a given class agree as to how attractive individuals of the opposite class are. Preferences are homotypic with respect to the second measure, referred to as ”character” i.e. all individuals prefer partners of a similar character. Such a problem may be interpreted as e.g. a job search problem in which the classes are employer and employee, or a mate choice problem in which the classes are male and female. It is assumed that attractiveness is easy to measure and observable with certainty. However, in order to observe the character of an individual, an interview (or courtship) is required. Hence, on observing the attractiveness of a prospective partner an individual must decide whether he/she wishes to proceed to the interview stage. Interviews only occur by mutual consent. A pair can only be formed after an interview. During the interview phase the prospective pair observe each other’s character, and then decide whether they wish to form a pair. It is assumed that mutual acceptance is required for pair formation to occur. An individual stops searching on finding a partner. This paper presents a general model of such a matching process. A particular case is considered in which character ”forms a ring” and has a uniform distribution. A set of criteria based on the concept of a subgame perfect Nash equilibrium is used to define the solution of this particular game. It is shown that such a solution is unique. The general form of the solution is derived and a procedure for finding the solution of such a game is given.