Nash equilibrium

I came across the concept of Nash equilibrium for games. As far as now I associated the name Nash to the movie "A beautiful mind", which I liked very much.
My professor of game theory at the university was so weird that I never really understood what he said. He looked like Bakunin and always had a stinky pipe in his hands.
But going back to the equilibrium, a game is said to be in such state when even if a player knew the strategies of all other players, he would not find any benefit in changing his strategy.
Described like this it sounds strange, but imagine I have two roads to drive to reach my office. If I know that everybody who wants to go there is taking one path and the other is empty (no traffic), I will choose the path without traffic. This game is not in Nash equilibrium, because I benefit by knowing other players' strategies. But if I know that the other drivers will equally distribute on both paths, than it does not really matter if I choose one or the other. This is an example of game in Nash equilibrium.

Probability distributions

I have to admit that my mathematics knowledge is really rusted... too bad!
But at least nowadays I do not have to search for information in my old books anymore: we have Google and Wikipedia! Hurraa!

The last thing which gave me troubles were probability distributions. I could still figure out what a discrete probability distribution could be (e.g. the probability of getting a '5' rolling a dice in the discrete interval 1 to 6 is 1/6), but I had no clue of what a continuous distribution is :(
Wikipedia helped again.
Probability of a continuous distribution is for example the probability that a tree leaf is 3,5cm long on a given continuous interval like between 3 and 4 cm.
With discrete distributions, the probability of an impossible event is 0 ( e.g. getting the result 3,5 on a dice), but the weird things with continuous distributions is that the probability can be 0 even if an event is not impossible!
Going back to the 3,5cm long leaf: how many chances do you have of finding such a long leaf? well... it is difficult to find out, because we can't count and add the probabilities.
Formally the value 3,5 has an infinitesimally small probability, which is statistically equivalent to 0. WOW!

eBay auctions on weekends...

I read an article "PENNIES FROM eBay: THE DETERMINANTS OF PRICE IN ONLINE AUCTIONS" by David Lucking-Reiley, Doug Bryan, and Daniel Reeves.
The article is quite old: it was written in 1999, when eBay was only 4 years old and available only in USA (I think, but I may be wrong).
What caught my eye was this chart!
It is a histogram of auction closings (doesn't matter wich kind) by day-of-the-week.
The authirs comment that "As one might expect for a consumer-oriented site like eBay, volume is heaviest on weekends."
This data contraddict my observations of what is going on today. I do not have as reliable data as they had, but the auctions I have seen are definetly less succesful on weekends!
Bidders tend to bid last minute (either they don't know the concept of proxy bidding or they refuse to use it) and on weekends they are not as much online as on weekdays from their offices!
I will try to investigate this points to get reliable data to check if I am right ;)

Payoff

I came across the concept of payoff... I never tought about it!
For example in a English (ascending-bid) auction the bidders who lose the auction have a payoff of 0. This makes sense, since they don't earn and don't pay anything.
What I never thought about is that the bidder who wins the auction has a payoff which is not equal to the amount he pays, but to the difference between how much he values the item and how much he pays for it!
Let's make an example: I always buy a beauty cream on eBay, which costs 19,99€ in the normal shops. If I can get that cream on eBay for 15€ (+1,85€ shipment), my payoff will be 3,34€.
The 3,34€ are the difference between my estimated value of the item and the money I pay for it on eBay. The question is: does it make sense to but the cream on eBay, take the risk of being cheated by the unknown seller or by the postal service which may lose the packet to save only 3,34€?
Well, for me yes, consider it is more than 15% discount on the shop price!
Perhaps the real question is if I really need the cream... but women can do almost anything for their beauty ;)

Trust

[eBay founder] Pierre M. Omidyar… hit on the idea of building a flea market in cyberspace – where people could buy and sell anything to anybody. There was one snag, though. How could he persuade complete strangers to trust one another enough to hand over merchandise or cash without ever having met? Omidyar’s solution was to devise a system where buyers and sellers can rate their experiences with different traders… That provided the assurance people needed to feel comfortable trading with one another – and it helped Omidyar’s eBay become the largest person-to-person auction site on the Web.

Source: Green and Browder [1998].

Study material

I am currently reading this: Why study auctions.

Most common auction types

Perhaps it's worth to mention that there are different kind of auctions and the most famous are:

1. the ascending-bid auction (also called English aution, open or oral) is perhaps the most famous, in which the bidders offers higher and higher prices until nobody offers more
2. the descending-bid auction (also called Dutch auction, since its most famous application is the sale of flowers in Nederlands) in which the price sinks until a bidder offers to pay the current price
3. the first-price sealed auction in which the bids are conveied in private form and the auction is won by the bidder who offers and pays the highest price
4. the second-price sealed auction (or Vickrey auction) in which the bids are conveied in private form and the auction is won by the bidder who offers the highest price, but pays just the price of the second highest bid plus a small increment.

There is an important theorem, the revenue equivalence theorem, that proofs that under some circumstances these 4 auctions have the same results. I am trying to understand it, but I am still not done (I need to refresh some mathematics :o !!!) I will let you know...

Paper: Vickrey Auctions in Practice

I found and read a very easy and well written paper by David Reiley: "Vickrey Auctions in Practice: From Nineteenth Century Philately to Twenty-first Century E-commerce"(available in internet, just google it).
I did not know that collecting stamps was such a old hobby (a bit boring... isn't it?).

A Vickrey auction (or second-price auction) is a auction where the bidder who offers the highest price wins the auction, but he's not expected to pay the full amount of his bid, just the sencond highest price plus a small increment (if the highest bid is 100€ by bidder A and the second highest is 90€ by bidder B, bidder A will win and pay 91€, if the increment is 1€).
This is for example the type of auction going on in eBay.

William Vickrey won (post mortem) the Nobel Price for Economics in 1996 for his studies on auctions theory.

Auctions at the seaside in Italy

Well, I guess the first aution I have ever seen was in Italy, in Lido degli Estensi, a seaside resort on the Northern Adriatic coast.
There there's a auction house on the main pedastrian street called Ariete which sells "art", for many many years now. What is "art" in this case? Well... just any crap you can imagine.
The owner of the house sits on a chair and talks the all time in a mike about how beautiful and rare the items are! He calls out the first price and, if there are any people watching, most of them start laughing more or less openly...
There are chairs for the potential bidders and they are often used by tourists to rest for a few minutes before continuing the evening stroll (auctions are held in the evening, since during the day everybody is on the beach). Nobody seems to care for the items offered, free chairs and free eintertainment are a good attraction.
I have never understood how this auction house can survive: I have never seen anybody bidding!
... but I have to admit that it is fun to have a look, while sitting on the chairs and eating an ice cream :)

why auctions?

Well, if you are wondering why I chose the topic auctions as subject for this blog, I can try to give you an answer.

My enthusiasm for auctions started with eBay. I consider eBay a genial idea, not only for the auctions going on there, but mostly because it made them available to everybody in a very easy way.
I started selling stuff on eBay. When I moved in a rented apartment in 2006, the former tenant left behind a lot of useless stuff (even condoms!) and I did not know what to do with it. I tried to give it away, but nobody was interested. I tried to put adds on local web sites, but again I could not reach anybody who wanted to have it.
Then I tried with eBay. I must admit that at the beginning I was a bit unconfortable with the idea that I have to pay money to put things on sale, but now I can say that this money is worth.
Since then I have 100% positive feed and 144 ratings... and a new hobby: auctions :)

here I am!

Hi everybody,
my name is Daria and I would like to use this blog to collect thoughts, ideas and information about my last hobby: auctions.
I am a completely newby in this field, but I find it fascinating! I hope I will find people who like me share this interest and I am sure we will have fun :)

Just a few words about me: I got a master in mathematics in 1998, but I cannot define myself a matematician. Since then I worked in the IT sector, first as a software developer and recently as a consultant.

I live in Europe in the beatiful city of Munich. My mother language is Italian, others are English, German, Spanish and a bit of Hindi.