Recall the second price auction game. Now suppose that there are three players, 1, 2, and 3, bidding for a single object in a second price auction. All three players value the object at 10, i.e., v1 = v2 = v3 = 10. For i = 1, 2, 3, let bi denote player i’s bid. The players are free to bid any price they like. The player with the highest bid wins the object, with ties broken by a fair lottery, and pays the highest bid among her opponents. Write down a bidding profile (b1,b2,b3) that constitutes a pure strategy Nash equilibrium (PSNE) of the game that have the following properties:

1) Write down a PSNE, in which NO player plays a weakly dominated action.

2) Write down a PSNE, in which player 3 wins the object with probability one. Argue that it is indeed a Nash equilibrium.