One bidder in 2nd price auction in second priced auctions, the highest bidder wins the auction and pays the price of the second highest bidder. What happens if there's only one bidder? That bidder would have won the auction, but does the winner pay his/her own bid? Or does the winner pay zero, imagining a second bidder with zero value bid?

Thanks
The purpose of a 2nd price auction (Vickrey Auction) is to encourage bidders to bid their true maximum willing payment for a good rather than the lowest price they expect will win the auction. The reason for this is because they pay the value of the unknown second bid they don't have to worry about bidding to high because the highest bid will always pay the exact lowest they would have had to pay in order to obtain the product and don't have to worry about overbidding.

For a auction to be called an auction there must be multiple bidders. If I know that I am the only bidder I would always just bid $.01 and get everything for free. To prevent this and other types of bidder collusion all auction houses have a minimum starting bid for a product usually determined by the seller. If no one is willing to pay more than the minimum then the product simply wont be sold. Individual rule for vickrey auctions differ depending on the venue but I imagine if only one bid is made then the price would default to the minimum bid set before the auction.