Why good guys are not selected by good girls??

ABSTRACT:

This note illustrates the negative impact on good guys
of the presence of bad guys in a market for relationships.
We make use of two simple examples based upon the
lemons model by Akerlof (1970). Firstly, we show that
the presence of bad guys can lead to no market equilibrium
in the sense that no trade occurs. Secondly, we provide a
simpler framework in which only bad guys get a relationship
and good guys are crowded out of the market.

1.INTRODUCTION

Getting into relationships with girls is more difficult for
good guys than for bad ones. We illustrate this point in
the context of a market for relationships.
The choice variable is whether to enter into a relationship.
The setup of the model is borrowed from the lemons
model of Akerlof (1970)1. It is usually assumed that
buyers and sellers in a market are both perfectly informed
about the quality of the goods sold in this market. This
assumption can be challenged if information is costly to
obtain. In the case of interest in this paper, information
is clearly costly to obtain. We think of guys as being
suppliers of and girls as being demanders for a relationship.
This assumption is made for convenience: in the real world,
good girls may also be affected by the presence of bad
girls if they supply a relationship and guys demand one.
Anyway, the story works for both sides, so that we proceed
with our assumption. Obviously, girls would want to know
whether a guy is good or bad to go out with. However,
knowing this requires a costly process of gathering
information from previous girl-friends which is highly costly
given the inherent conflicts that are implied. This asymmetric
information leads to a suboptimal social equilibrium.

2.FIRST MODEL: NO TRADE TAKES PLACE

We draw largely upon Tirole (1988). In a market for
relationships, we assume that there is a population of guys
and a population of girls which are both normalized to unity.
The guy has monopoly power over a relationship whereas
the girl demands such a relationship. The relationship is
characterized b a parameter B> 0. We understand that
a higher parameter is equivalent to a higher level of quality
of the relationship. A status quo is defined as a situation
where both the guy and the girl remain single.

The guy’s surplus in the case of status quo is Q1 and it is
equal to p if a relationship takes place. The girl’s surplus
in the case of status quo is 0 and it is Q2 − p if a relationship
takes place. In our context the price can be interpreted as
the foregone free time for shopping, haircutting, and so on,
that the girl must accept. Typically, girls are more romantic
than guys and therefore, we will assume that the marginal
valuation for quality is higher for the girl than for the guy,
that is, Q2 > Q1. Whereas the guy knows perfectly, the girl
only knows that Q2 {0, 1} with probabilities
Pr(B=0) = Pr( B= 1) = 0.5 ...(1)
where 0 implies a low-quality relationship and 1 a
high-quality relationship.
So, the guy can be good or bad depending on the quality
of the relationship that he supplies. The girl maximizes her
expected surplus given by
(Q2)Be − p ...(2)
where Be is the expected quality of a relationship.
Participation of the buy in the trade requires p >=(Q1.B).
In other words, the guy would get into a relationship if and
only if B lies in [0,P/Q1].
Therefore, the girl’s expected quality given that trade
occurs is given by
Be(p) = 0.5 · 0 + 0.5 ·P/Q1=P/2(Q1) ...(3)

The girl will buy a relationship if and only if
Q2Be(p)>=P;
i.e. Q2.P/Q1>=P
1.e. Q2>=2(Q1)

If tastes do not differ too much, so that Q2 < 2Q1, there is
no equilibrium. For every , a transaction which is clearly
socially desirable will not take place. Both the girl and the
guy remain single. This result would not obtain if there
were only good guys in the market for relationships.

3.SECOND MODEL:ONLY BAD GUYS GET A RELATIONSHIP

The result obtained in the previous section is extreme in
the sense that no relationships take place. This section
presents a simple example where only bad guys will get
into relationships whereas good guys are crowded out. We
assume a market with 100 guys who supply a relationship
and 100 girls who demand a relationship. As before, it is
common knowledge that 50 guys are good, thereby
supplying a good relationship and the other 50 guys are
bad, therefore supplying a bad relationship. Each guy
knows his quality, i.e. whether he is good or bad, but
each girl does not know the quality of each guy with
certainty. We assume that each bad guy is ready to
sell himself for 100 units of time and a good guy for
200 units of time. The girls are willing to pay 120 units
of time for a bad guy and 240 units of time for a good guy.
Suppose now that there is no asymmetric information.
Each girl can observe the quality of each guy. The
equilibrium price for a bad relationship will lie between
100 and 120 units of time while the equilibrium price for
a good relationship will be between 200 and 240 units
of time. There is no market failure and the equilibrium is
socially optimal. However, what happens when there is
asymmetric information, i.e. when the supply side knows
something that the demand side cannot observe?
Well, the girls have to guess how much each guy is worth.
We assume that since any guy has an equal probability of
being a good guy or a bad guy, each girl is ready to pay
the expected value of the guy, that is
p = 0.5 · 120 + 0.5 · 240 = 180


At this price, only the bad guys would be willing to supply
a relationship and thus, only relationships with bad guys
are sold in the market. But then, if a girl is certain that
she would get a bad guy, she would not pay 180 units of
time but the equilibrium price between 100 and 120 units
of time. For such a price, only bad guys get a relationship
with a girl! Moreover, half the girls remain single.

The source of the market failure is an externality between
good and bad guys. This result is also rather extreme in
that it shows that only bad guys have a relationship and no
good guy does. Obviously, we know that this is not true so
that the market failure is not as bad as predicted by our
little model.
However, this approach helps understanding why some
guys of whom everyone says they are nice still
remain single... ;))