Response to reader: Since we don't know how much an auction winner payed for their bids how do we know if they got a good deal?

An anonymous reader left the following comment on a post I made about a Swoopo auction in which the winning bidder lost money and would have been better off purchasing the iPod he won at the retail price. I decided to post my response here instead of in the comments because I think many readers will find this argument interesting. Here is my original post and below is the comment:

"Swoopo also auctions of bids. Hence, you assume that he paid $108 in bids, but he may have purchased the bids at a substantial discount. 50 bids recent sold for $3.62. It is likely that his cost of bidding was below $43.60 and he earned positive profits."

You make a good point Anonymous, the winner may have paid less than retail price for his bids which would increase the value he received from winning. However, your argument is incorrect because in actuality it is highly unlikely the winner spent less than $43.60 on bids, as you suggest. Here is problem with your argument:

If the bidder paid $43.6 in bids (which is, as you point out, the most he could have paid to have received a favorable price on the iPod)and he cast 144 bids ($108/.75), he would need to be paying $0.30 per bid (43.6/144) to stay below $43.6. This means he would need to have won the bidpack in your example (and several more just like it) with just 15 bids or fewer.

Here is where 15 comes from:

3.62 +.75(X) = 50*.3

Where X is the number of bids cast to win (rounded), .75 is the price of a bid, 3.62 is the cost of the 50 bid bidpack for the winner, 50 is the number of bids won and the .3 is the required price per bid won.

Winning a 362 bid auction with 15 bids (4% of bids cast) is unlikely. It's possible but I don't think you can argue this is the norm and not the exception. I'm not saying winning is based on odds, it's not, but people tend to win when they demonstrate their willingness to win at all costs, ie exhaust their competition - a feat than cannot be accomplished with 15 bids. People do win with only one bid, but these situations... are highly, highly unlikely, especially on Swoopo, the most popular penny auction site in the world.

Let’s take it one step further. Say this bidder is a repeat player and acquires all of his bids by winning bidpack auctions (never buying any) and let’s assume in doing so the price per bid he receives from winning bidpack auctions is $0.30. If we use this as the price per bid cast for him to win the bidpack auction in your example he would need to win the bidpack with the following number of bids or fewer:

3.62 +.3(X) = 50*.3

X = 38

He would need to win the bidpack auction with 38 bids or fewer to hold his price per bid at or below $0.30. Winning a bidpack auction in which 362 bids were cast with 38 bids (10.5% of bids cast) is still highly unlikely and even more unlikely on a repeat basis – which is required for his price per bid placed to stay at $0.30.

This outcome also fails from a theoretical standpoint. If users could expect, with a high degree of certainty, to win bidpack auctions at a cost per bid won of $0.30 on a regular basis they would never buy bidpacks at the retail price. Swoopo would be losing money on almost every single auction and would also have to be auctioning off far more bidpacks than we see them doing.

Note: the auction for the iPod in my earlier post is from a period of time when Swoopo charged $0.75 per bid, the auction for the bidpack Anonymous cites in his comment is from a more recent auction after Swoopo started charging $0.6 per bid. The change in bid prices would likely alter the outcomes of these two auctions slightly, but the general argument still holds.

Anonymous makes a good point that we don't know how much other bidders paid for their bids or how this impacts their bidding decisions. However, in the case of the iPod auction discussed here, the winner almost certainly lost money.
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