Consider the following auction (known as a "Second Price" or "Vickrey" auction): an object is auctioned off to bidders. Bidder 's valuation of the object (in monetary terms) is . The auction rules are that each player submits a bid (a real number) in a sealed envelope. The envelopes are then opened and the bidder who has submitted the highest bid gets the object but pays the auctioneer the amount of the second highest bid. If more than one bidder submits the highest bid, each gets the object with equal probability. Show that submitting a bid of with certainty is a weakly dominant strategy for bidder . Also argue that this is bidder 's unique weakly dominant strategy.