A Model of Partnership Formation with Friction and Multiple Criteria - Search Theory: A Game Theoretic Perspective - page 259

individual should not continue searching until he finds his/her best possible partner.
The following assumptions are made:
(A) We consider the formation of long term relationships between two classes of
player (e.g. marriage, employment). When a partnership is formed, the two
individuals involved leave the population of searchers. Henceforth, we will
refer to these two classes of players as males and females.
(B) Interactions are bilateral and occur between a male and a female. The length of
an interaction is assumed to be small (effectively of zero length) compared to
the time between interactions. The pair must decide whether to form a partner-
ship or continue searching. Mutual acceptance is required for a partnership to
form. Individuals cannot return to a previously met prospective partner.
(C) When an individual leaves the population, he/she is replaced by a clone, i.e. an
individual of the same sex, attractiveness and character enters the population of
searchers. Hence, the joint distribution of attractiveness and character is fixed.
It might be more realistic to consider a steady-state model in which individuals
enter the pool of searchers at a steady rate according to their sex, attractiveness
and character. However, due to the novelty of the approach used and some of
the issues involved in deriving equilibria, for the present we adopt the simpler
clone replacement approach. It is intended that the steady state approach will
be adopted in future work.
(D) It is assumed that time is discrete and the search costs of males and females per
unit time are c 1 and k 1 , respectively. At each moment in time a player encoun-
ters a prospective partner. We assume random matching, i.e. the attractiveness
and character of the female encountered by a male is chosen at random from
the joint distribution of attractiveness and character among females. Using the
assumption of clone replacement, it is also easy to adapt the model to assume
that encounters occur as a Poisson process. It may be assumed that individu-
als find prospective partners at rate 1 and males and females pay search costs
of c 1 and k 1 per unit time, respectively. Empirical evidence on search costs
in real-life job search problems abounds in the literature. For instance, Peter-
son et al. [ 30 ] consider job search costs to be the primary cause of 'sticky'
wages and low labour market mobility, when contrasting the European and
US labour markets. Devine and Piore [ 12 ] also present empirical evidence on
search costs, and in the extensive literature incorporating job search costs into
macroeconomic models, Andolfatto [ 5 ] is representative.
(E) Encounters have two stages. In the first stage, both individuals must decide
whether they wish to date based on the attractiveness of the prospective part-
ner. For convenience, it is assumed that these decisions are made simultane-
ously. Dating only occurs by mutual consent. The costs of dating to males and
females are c 2 and k 2 , respectively. During a date, each observes the character
of the other and decides whether to accept the other as a partner. Again, it is
assumed that these choices are made simultaneously. A partnership is formed
only by mutual consent. In some scenarios—for example, when character is
unimportant—it might pay a female to immediately accept a male without
dating. However, to keep the strategy space as simple as possible, it is assumed