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In a second price auction, what occurs if two bidders bid the exact same amount on a non-divisible item. For instance, let's say these are the bids for object A:

Bidder W - $9.00 
Bidder X - 11.00 
Bidder Y - 11.00 
Bidder Z - 10.00 

Who has won this auction and what price do they pay?

Also, let's look at a somewhat similar scenario. Here are the bids for object A:

Bidder W - $9.00 
Bidder X - 10.99 
Bidder Y - 11.00 
Bidder Z - 10.98 

Here Bidder Y has won the auction but will end up paying almost the exact same amount as their original bid. I would imagine that neither Bidder X or Bidder Y would be very satisfied with the outcome of the auction and would be unlikely to return in the future.

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  • $\begingroup$ Is this a sealed bid auction, or one where the bidders can bid again? $\endgroup$ Mar 6, 2013 at 17:01
  • $\begingroup$ I hadn't thought to include that. Let's say it is a once daily auction where all the bids are sealed. The auction will repeat again tomorrow and all the bidders will know yesterday's winning price. $\endgroup$ Mar 6, 2013 at 17:08
  • $\begingroup$ And then on a particular day the auction ends and the item is sold? Based on the last day's bids, or on the highest of the days leading up? If the last day's, all the previous days don't matter except as advertising. $\endgroup$ Mar 6, 2013 at 17:11

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You would have to check the rules, but the sensible thing to do in the first case is flip a coin and sell to either X or Y at 11. It is like one or the other bid $11-\epsilon$. If the bids are sequential I think you would award it to the first to bid $11$ (and usually not accept the next bid unless it was greater than $11$)

You are right that the second case is very similar. There may be a minimum increment for a bid, which your example indicates is 0.01. If more than one bidder have very similar values for the item this is what happens. The idea is that each bidder is encouraged to bid his true value. If they did that, Y is making a profit (true, of only 0.01). X can now bit 11.01, but then would take a loss of 0.02 if the 10.99 bid were truthful. Y may be disappointed, but that's life.

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