the battle of the sexes the game in this exercise, called battle of the sexes, is
an oft-quoted example in game theory (see also example 4.21 on page 98). the
name given to the game comes from the story often attached to it: a couple is trying
to determine how to spend their time next friday night. the available activities in
their town are attending a concert (c), or watching a football match (f). the man
prefers football, while the woman prefers the concert, but both of them prefer being
together to spending time apart.
the pleasure each member of the couple receives from the available alternatives
is quantified as follows:
from watching the football match together: 2 for the man, 1 for the woman.
from attending the concert together: 1 for the man, 2 for the woman.
from spending time apart: 0 for the man, 0 for the woman.
the couple do not communicate well with each other, so each one chooses where he
or she will go on friday night before discovering what the other selected, and refuses
to change his or her mind (alternatively, we can imagine each one going directly
to his or her choice directly from work, without informing the other). depict this
situation as a game in extensive form.