Consider that there is one auctioneer who would like to sell one commodity and

there are 5 individuals, 1, 2, 3, 4, and 5. The auctioneer will apply the following

tie-breaking rule: If there are multiple bidders who announce the highest bid,

then select the bidder with the smallest index will be picked up as the winner.

(For instance, let bi = bj > bk for any k 6= i, j. Then, i is the winner if and only

if i

v1 = $1500; v2 = $1000; v3 = $2000; v4 = $900; v5 = $800.

Then, answer the following questions.

(1) Suppose that the auctioneer will apply the 2nd-pricing auction rule.

(1-1) Then, what strategy profile would be the dominant strategy equilibrium? Is this dominant strategy equilibrium unique in this game? Also show

the reasons of your answers.

(1-2) Is there any other Nash equilibrium in this game? Specify what strategy

profile would be a Nash equilibrium.

(2) Suppose that the auctioneer will apply the 1st-pricing auction rule. Then,

specify the set of Nash equilibria in this game.