A Model of Partnership Formation with Friction and Multiple Criteria - Search Theory: A Game Theoretic Perspective - page 280

In addition, it would be useful to investigate how the utility functions, together
with the relative costs of searching and interviewing, affect the importance of at-
tractiveness and character in the decision process. It should be noted that using
attractiveness as an initial filter in the decision process will lead to attractiveness
becoming relatively more important than character, especially if the costs of dating
are relatively high.
It would also be useful to adapt the algorithm to problems in which the
distribution of character is not uniform and/or the set of character levels do not
form a circle. In this case, it is expected that individuals of extreme character will
usually be less choosy than those of a central character for a given level of attrac-
tiveness. Two major problems result from this. Firstly, the form of an equilibrium
will be more complex than the form of the symmetric equilibrium given here. Any
algorithm to derive an equilibrium in this case will certainly be more complex than
the algorithm outlined in this chapter, which uses the fact that the problem can be
reduced to a sequence of one-sided problems. The unique equilibrium derived here
would be useful as a point of reference.
Finally, it would be interesting to consider games in which the distributions of
traits and/or search costs depended on class. In this case, it would be natural to
assume that the equilibrium is asymmetric with respect to class. In the spirit of the
derivation of equilibrium points in the classical matching problem (see Gale and
Shapley [ 18 ]), it would be interesting to see whether equilibria analogous to male-
choice and female-choice equilibria exist. For the types of model considered here,
to find a male-choice equilibrium we would try to maximize the expected utility of
males while adapting female choice to male choice.
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