What I specifically don't understand is:

1) Why: When G(v1) = v1, with v1 and v2 uniformly distributed over [0,1] , WHY does E[v2 |v2 < v1] = (v1)/2 , i do not understand how they get v1 over 2.

2) Why: when we move from 2 to N people with distributions over [0,1], why does G(v1) = (v1)^N-1 ? I don't understand this definition.

Lastly, 3) So when G(v1) = (v1)^N-1, E[v2|v2<v1] = ((N-1)/N)*v1

Please please help me, ask if anything is unclear. Thank you SOOO MUCH.