Not everyone loves statistics, we’ll be the first to admit that! however many of you have requested that we show some stats about penny auctions. When you use these statistics correctly, you will be able to see a pattern and hopefully it will help you choose the right moment when it comes to bidding.

There are various posts and pdfs around the internet that have conducted studies to determine exactly how penny auctions work. They show the percentage of winning, the average amount of bids it takes, deep analysis of the buy it now feature and much more. By using this information, it can really give you the edge over your competitors.

Introduction

A typical penny auction may sell a new brand-name digital camera, at starting price 0 and timer at 1 minute. When the auction starts, the timer starts to tick down and players may submit bids. Each bid costs $1 to the bidder, increases price by $0:01, and resets the timer to 1 minute. Once the timer ticks to 0, the bidder who made the last bid can purchase the object at the current price. Note that the structure of penny auctions is similar to dynamic English auctions, but with one signicant dierence. In penny auction the bidder has to pay signicant price for each bid she makes. Both the name and general idea of the auction is very similar to the dollar auction introduced by Shubik (1971). In this auction cash is sold to the highest bidder, but the two highest bidders will pay their bids. Shubik used it to illustrate potential weaknesses of traditional solution concepts and described this auction as extremely simple, highly amusing, and usually highly protable for the seller.Read more – http://toomas.hinnosaar.net/pennyauctions.pdf

We will first look at a case where the price increment ” = 0. This is called \Free auction” (if P0 = 0) or \Fixed-price auction” (if P0 > 0) in Swoopo.com. One could also argue that this could be a reasonable approximation of a penny auction where ” is positive, but very small, so that the bidders perceive it as 0. In this case the auction very close to an innitely repeated game, since there is nothing that would bound the game at any round17. After each round of bids, bid costs are already sunk and the payos for winning are the same.

This is a well-dened game and we can look for SSSPNE in this game. As argued above and proved in the Appendix A, the SSSPNE is fully characterized by a pair (^q0; ^q), where ^q0 is the probability that a non-leader will submit at round 0 and ^q the probability that a non-leader submits a bid at any round after 0. Let ^v; ^v be the leader’s and non-leaders’ continuation values (after period 0). The following theorem shows that the SSSPNE is unique and gives full characterization for this equilibrium.

Some of these statistics can be quite confusing, we highly recommend taking a read at the full PDF however because it goes into more detail about what these stats actually mean. It brings a whole new concept to the meaning of knowing how penny auctions work. Sure most people know the basic principles. But when you have cold hard facts and stats, this can really give you the edge.

Your average penny auction bidder (In fact it’s about 80-90%) hasn’t done much homework on penny auctions. What I mean by that is that they possibly watch a video on “How penny auctions work” and thats it! that’s all the knowledge they think they will need before they sign up to a penny auction site and start bidding.

Here is a better PDF that is much more clear, the experiment is also conducted using the site “Swoopo” which now no longer exists but the methods can still be applied to any penny auction site because they all share the same model:

Given the specification to this point, the model permits a very wide class of equilibria. Below, I will attempt to address the structure of the general equilibria. However, for now, I will limit my scope to those equilibria in which there is non-zero probability of the auction reaching each stage k ¯k. Denote by pk the probability that there is no kth bid placed, conditioned on there being k − 1 bids placed. In other words, pk is the probability that the auction terminates with price d(k − 1). Therefore, pk envelops the behavior of all n players insofar as it represents the collective probability of none of them bidding at the kth stage. Now, with ˆk = ¯k, we consider equilibrium behavior. Recall, for any k > ¯k, we have pk = 1, as no agents will bid and the auction terminates with certainty. For k ¯k, since there is nonzero probability of the auction reaching that stage, at least one player must be mixing over his strategies: bid or not bid. Each of these agents mixing in the equilibrium must be made indifferent over his choices. This defines for 1 < k ¯k the indifference condition: (v − kd)pk+1 − b = 0.

Read more – http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.167.6018&rep=rep1&type=pdf

Again, it may seem quite confusing which is why we recommend reading the whole document, it’s a very thorough experiment and really explains exactly what the rates of winning on penny auction sites are. There are over 60 pages in this document, all of which are a great read, the document even goes into detail about early bidders and bidding timers which we have talked about on penny decisions.

So if you’re looking to join a penny auction site, we highly recommend reading some of these documents because they go to great lengths to explain exactly how everything works. Sure, the stats can be a bit long winded and confusing but is still worth taking a look.

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