Two players participate in a first price sealed bid auction. Both players agree that the object has value $100 with probability 1/2 and value 0 with probability 1/2. However, player 2 is told the value of the object before bidding, while player 1 is not. The auction has a tie-break rule: if the two players submit identical bids, the object goes to the second player.

i. Show that there is not a pure strategy Bayesian Nash equilibrium.

ii. The mixed strategy equilibrium is such that player 2(0) (player 2 that knows that the value is zero) bids zero. Player 2(100) plays a nonatomic mixed strategy, while player 1 plays a mixed strategy that puts an atom on zero. Find such an equilibrium.