One method of exposing player to player trust is to have them fill out what is commonly referred to as the "Foxhole Test."  Each player fills
out q form like the one below.  The individual filling out the form is
in the foxhole.  He/She fills in the other 3 spots with the spot directly
in front is the person you trust the most to protect you.  The person on the left is second in terms of trust and the person on the right of
the person in the foxhole is the third most trusted.  These forms are
filled out and given to the coach.  The coach collects all the forms
and, if he/she wants tallies the results.  You (as their coach) can do
what you want with the results.  Personally, I would not share the results with the individual players.  I would consider sharing with 
selected individuals if I believed it was beneficial to the team.