4. Consider a first-price, sealed-bid auction where an indivisible good is sold. Assume that the bidders' valuations are independently and identically distributed on [0, 1] with distribution function F(z) = z%. There are n > 2 bidders. Simultaneously, each bidder submits a bid b; > 0. The agent who submits the highest bid wins. If there are > 2 bidders submitting the highest bid, then the winner is determined randomly among these bidders each has probability 1/k of winning. Show that 2n2 2n1 a strategy profile is a Bayesian Nash equilibrium of this auction. if every bidder adopts the strategy of bidding times her valuation, then such