A Model of Partnership Formation with Friction and Multiple Criteria - Search Theory: A Game Theoretic Perspective - page 279

The form of a symmetric equilibrium profile which satisfies various criteria based
on the concept of a trembling hand perfect equilibrium was derived and an algorithm
to find such a profile described. These criteria are a generalization of the optimality
criterion used by McNamara and Collins [ 28 ] to define the unique equilibrium in
the classical two-sided job search problem. It is shown that such an equilibrium
exists and is unique (assuming that if an individual is indifferent between accept-
ing or rejecting a prospective partner at any stage, then he/she accepts). Although
the equilibrium derived here does have some similarities to the equilibrium derived
by McNamara and Collins [ 28 ], it is essentially different, since it is not a block
separating equilibrium.
The use of this combination of preferences would seem to be logical in rela-
tion to job search and mate choice. Although there is no perfect correlation in in-
dividuals' assessment of the attractiveness of members of the other class, there is
normally a very high level of agreement, particularly among males in mate choice
problems. These 'mixed' preferences seem to be both reasonably tractable within
the framework of searching for a partner within a relatively large population and al-
low a general enough framework to model the preferences of individuals reasonably
well (although it would seem that modelling character as a one-dimensional vari-
able is rather simplistic). By using a larger number of types, we could approximate
continuous distributions of attractiveness and character.
For simplicity, it was assumed that individuals know their own attractiveness and
character, whereas in practice they may have to learn about these measures over
time (see Fawcett and Bleay [ 15 ]).
Also, it was assumed that individuals are able to measure attractiveness and
character perfectly, although at some cost. It would be interesting to consider dif-
ferent ways in which information is gained during the search process. For example,
some information about the character of a prospective partner may be readily avail-
able. Hence, an improved model would allow some information to be gained on
both the attractiveness and character of a prospective partner at each stage of an
interaction.
In terms of the evolution of such procedures, it is assumed that the basic
framework is given, i.e. the model assumes that the various search and dating
(interview) costs are given. Hence, this model cannot explain why such a system
has evolved, only the evolution of decisions within this framework.
Individuals may lower their search costs by joining some internet or social group.
Such methods can also lead to biasing the conditional distribution of the character of
a prospective partner in a searcher's favour. It is possible that dating (interview) costs
are dependent on the types of the two individuals involved. For example, two indi-
viduals of highly different characters might incur low dating costs, as they realize
very quickly that they are not well matched.
Also, the ability to incur dating costs may well transfer information regarding the
attractiveness and/or character of an individual. In this case, it may be more costly
to successfully date highly attractive prospective partners, since they would only
accept partners who can pay high dating costs (i.e. are attractive).