A Model of Partnership Formation with Friction and Multiple Criteria - Search Theory: A Game Theoretic Perspective - page 256

17.1 Introduction
This chapter presents a game theoretical sequential search problem modelling
partnership formation based on two traits. There are two classes of individual, and
each individual wishes to form a partnership with one of the opposite class. Each in-
dividual observes a sequence of potential partners. Mutual acceptance is required for
a partnership to form. On finding a partner, an individual ceases searching. One mea-
sure describes 'attractiveness'. 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.
For convenience, it is assumed that individuals know their own attractiveness and
character. Also, the distributions of character and attractiveness are assumed to be
discrete with a finite support, and constant over time.
Together, the attractiveness, character and the class of an individual determine
their 'type'. Individuals can observe the attractiveness and character of prospec-
tive partners perfectly. However, in order to measure character, a costly interview
is required. In addition, individuals incur search costs at each stage of the search
process.
At each moment an individual is paired with a prospective partner. First, both
individuals must decide whether they wish to proceed to the interview stage on
the basis of the attractiveness of the prospective partner. The final decision on pair
formation is based on both the attractiveness and character of the prospective part-
ners. Mutual acceptance is required for an interview to occur and a pair to form.
At equilibrium, each individual uses a strategy appropriate to their type. The set of
strategies corresponding to such an equilibrium is called an equilibrium profile.
Such a problem may be interpreted as a mate choice problem in which the classes
are male and female, or a job search problem in which the classes are employer and
employee. The assumption that attractiveness can be observed very quickly, but an
interview (dating) is required to observe someone's character is obviously a simpli-
fication. However, in the case of human mate choice many traits that can be thought
of as defining attractiveness (physical attractiveness, employment, economic sta-
tus) are usually measured quickly, whilst observation of traits defining character
(political and religious views, tastes and emotions) are generally more difficult to
measure.
17.1.1 Related Literature
Our model has a resemblance to 'speed dating' models recently developed and
tested by Fisman et al. [ 16 ]. The types of preferences we study have been ana-
lyzed (in continuous time) by Marimon and Zilibotti [ 26 ]. They found that these
types of preferences, in this context, were quite tractable and somewhat equivalent to