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 b,- = (23- > bk for any k 7E 2', j. Then, 2' is the winner if and only if z'