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Solicits dates with prospective
Attractiveness
partners of attractiveness
Expected Utility
6
{5,6}
7/2
5
{5,6}
10/3
4
{ 3,4,5,6 }
3/2
3
{3,4}
4/3
2
{ 1,2,3,4 }
−
1/2
1
{1,2}
−
2/3
14/5
Table 17.1
Brief description of the symmetric equilibrium for the example considered
0
{ 0,1,2 }
−
We wish to derive an equilibrium which reflects this inherent symmetry. Suppose
a type
[
,
]
male solicits a date with a female of attractiveness
k
and pairs with a
female of type
i
j
[
,
]
[
,
]
female should be willing to date a male of
attractiveness
k
and pair with a male of type
k
l
. Firstly, a type
i
j
male
should solicit a date with a female of attractiveness
k
and pair with a female of type
[
[
k
,
l
]
. Secondly, a type
[
i
,
6
−
j
]
k
,
6
.
It is expected that males of type
−
l
]
have the highest expected utility from
search and so we can treat the problem they face as a one-sided problem. However,
it is unclear whether in a specific problem individuals of type
[
6
,
3
]
[
6
,
2
]
or those of type
[
should have the higher expected utility from search at such an equilibrium.
Hence, it is unclear how the algorithm should proceed.
In order to solve more general problems, the algorithm presented in Sect.
17.8
must be further developed. However, it seems that the general approach of solving a
sequence of appropriately defined one-sided problems could be useful in deriving a
strategy profile which is very similar to an equilibrium strategy profile (see Ramsey
[
32
] for a similar approach). Also, the form of the general problem and the use-
fulness of such an approach indicate that if there are multiple equilibria, then the
behaviour observed at such equilibria should be qualitatively similar.
5
,
3
]
17.10 Conclusion and Directions for Further Research
This chapter has presented a model of partnership formation where both common
and homotypic preferences are taken into account. The preferences of all searchers
are common with respect to the attractiveness of prospective partners and homotypic
with respect to character. Attractiveness can be assessed immediately, but in order
to assess character a costly date (or interview) is required.
We have considered a particular type of such problems in which the distribution
of attractiveness and character, as well as search and interview costs, were
independent of the class (sex) of a player. Character was assumed to form a cir-
cle, such that the 'extreme' levels of character are neighbours. For convenience, the
supports of attractiveness and character were assumed to be finite sets of integers.
The distribution of character is uniform.
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