In my example we have 2 bidders, one with a higher valuation for the object than the other.
In order to find a N.E. we first made some observations:
1) There cannot be atoms at $b_i>0$
2) It cannot happen in a N.E. that both bidders place atoms on $0$
3) If bidding is contiuously mixed on some interval, then the bidding of the bidders must go down to $0$
4) The bidder with the lower valuation needs to put an atom on $0$
5) The bidder with the lower valuation will have to make zero profits in the Equilibrium
I don't really understand 4) and 5)
Why isnt is possible, that the bidder with the lower valuation bids in an interval between $0$ and his valuation?
Why does he have to make zero profits?