Finding subgame-perfect Nash equilibrium in the Trust game I am facing a game theory problem which is as follows:
An experiment was designed to study individuals' propensity to be trusting and to be trustworthy in a task called the investment game. In this game two subjects are each given 3 dollars as a show up fee.
One
of
the
subjects
is
told
that
he
or
she
will
be
decision
maker
one
(DM1),
and
can
send
an
amount
(0 dollar,
1 dollar,
2 dollar
or
3 dollar)
to
the
other
subject
(decision
maker
two,
DM2).
The
rules
are
simple.
Every
dollar
sent
will
be
doubled
by
the
experimenter
before
it
reaches
DM2,
who
then
gets
to
decide
how
much
of
the
doubled
money
to
keep
and
how
much
to
send
back
to
DM1.
After
DM2’s
decision
the
game
is
over
and
subjects
leave.
The
experiment
is
double-blind
meaning
that
neither
the
subjects
nor
the
experimenter
knew
who
was
matched
together,
or
what
subject
made
what
decision.
In order to analyze this problem, I have drawn the extensive and normal forms which are showed [here][1] and [here][2].
I find no matter what kind of choice each subject choose, they all choose to play either (0,0) or (3,3) in the Nash equilibrium.
Now the question is know how to find subgame-perfect Nash equilibrium in terms of normal form and extensive form?
Is the normal form of the Trust game a symmetric game?
normal form link  http://farm9.staticflickr.com/8426/7814582114_02459a1ef8.jpg
extensive form link  http://farm9.staticflickr.com/8304/7814582210_85db97fb45.jpg
 A: To find any Nash equilibria, fix one player's choice and choose the option that maximizes the other player's outcome.  For instance, suppose DM1 chooses 0, corresponding to the first row of your table.  Then DM2 is looking at pay-offs of 3 (by choosing 0), 2 (by choosing 1), 1 (by choosing 2), and 0 (by choosing 3).  In this situation, DM2 chooses 0, giving the maximum payoff of 3, assuming DM1 chose 0.
In the same way, for each choice that DM1 makes, DM2's payoff is optimized by choosing 0 (that is, in each row the second number of each ordered pair is greatest in the first column).  We say DM2 has a dominated strategy of choosing 0.
From the perspective of the other player, suppose DM2 chooses 0.  The DM1 chooses 0 since the resulting 3 is the greatest payoff in that column.  For every fixed choice of DM2, DM1's payoff is optimized by choosing 0 (in each column the first number of each ordered pair is greatest in the first row).  So DM1 also has a dominated strategy of choosing 0.
That means the Nash equilibrium occurs when both players choose 0, giving them each a payoff of 3.  
The concept of Nash equilibrium follows from assuming that you have no say over what the other player chooses.  This is similar to the prisoner's dilemma, which also has a sub-optimal Nash equilibrium.  Here, if the players could trust each other, they could each do much better by both choosing 3, giving each of payoff of 6.  But if you believe your opponent will choose 3, you can get a payoff of 9 by choosing 0 instead, which gives your opponent 0 -- that's the trust aspect. 
