An implicit assumption when we studied the 2nd price auction is that no two bidders have the same valuation. A standard specification is that if two (or more bidders) have the same bid (and this is the winning bid) then the winner will be picked randomly. Is still a dominant strategy to bid truthfully in the 2nd price auction under this specification? Provide a counter-example (that shows that a bidder can be better of not bidding her valuation) or a proof that shows it is still a dominant strategy.