Wednesday, September 29, 2010

Game Theory - Lesson 1

How to sell hundred dollars in two hundreds
and even more.


Suppose someone offers to sell Hundred-dollar in an Auction under these conditions: Whoever offers the highest price, of course wins, second place proposal will pay the bid and left empty-handed. What will happen at the auction?

Many people told me that if I offered a hundred shekels at an auction I certainly lose money and therefore it does not make sense to do that. After all, why would intelligent person offer more than a hundred dollars for the hundred i like to sell? Surprise-Surprise, as in many cases in Game Theory your intuition is wrong, it turns out that because the rules of the game and its dynamics i can make real money in that auction.

Lets see what would YOU do in that auction, will you offer one dollar to try and win a hundred? of course, why wouldn't you? so you try to win and offer one dollar. Well, that is exactly what the man next to you think and he offers two dollars. Now, you are lossing, not just the hundred dollars but another dollar of your own because you come second place (see the Auction rulls again), at this point its better for you to raise to three dollars (and try to win 97$). The man next to you come to the idea you just had (he is second place now) and raise to four dollars. How does it ends?

The same way the game continues until one of you stand on 99$ and the other on 100$. Notice that at this point I'm not going to loose, I'm already earned 99$! 100$ offer plus 99$ for second place, but, hey ... i want more!

Lets say that the game stops here. One of you pays 100$ for my hundred and the other pays 99$ for nothing! If you where the later, will you offer 101$ ? if you do you will only loose one dollar (see why?), try to think what each of you will do next... hint: it doesnt change alot, and I will have more money.

The truth is that simply does not pay to play this game. That is what Game Theory tells us, if you see that kind of a game, stay away! you can't win! You can earn only if your competitor decides to quit under a hundred dollars and it is definitely high risk to take. All in all, these only one hundred dollars.

Try to think what would happen if the amount offered was a million dollars.

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