Game Theory - Lesson 2 The Prisoners Dilemma and how it affect your life

Prisoner's dilemma" - is a very famous game in Game Theory. Much has been written and spoken about it and although its mathematic nature lots of academic studies tries to use it to understand phenomenon and side affects in people's behavior today

The game has many versions, in the original version two suspects, Mr. A and Mr B, are arrested by the police. The police have insufficient evidence for a conviction, and, having separated the prisoners, visit each of them to offer the same deal. If one testifies for the prosecution against the other (defects) and the other remains silent (cooperates), the defector goes free and the silent accomplice receives the full 20-year sentence. If both remain silent, both prisoners are sentenced to only one year in jail for a minor charge (maybe as careless driving). If each betrays the other, each receives a fifteen-year sentence (25% deduction in appreciation for your cooperation.). Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?

The "game" can be summarized in the following table:

	Mr. B
Mr. A	cooperates defects cooperates Both sentenced for one year Mr. A - Free Mr. B - 20 years defects Mr. B - Free Mr. A - 20 years Both sentenced for fifteen years

Ostensibly, there is no dilemma - each player must choose to keep quiet and thus ensure the minimum sentence of one year they may reap even one-third for good behavior and Hop! they are out. To understand the dilemma try to understand what was happening in the head of one of the prisoners say Mr. A.
When he thinks to himself what to choose he is trying to predict what Mr. B will select

"If Mr. B will keep quiet so it is better for me to talk - so I'll be free. If Mr. B will will speak - of course it's better for me to talk and i will not get the maximum punishment."

It seems that for every choice Mr. B will make, Mr. A will talk. This game is of course symmetric, so there is no difference between what Mr. B would think and will select to speak.
Thus, the game that seems quite simple becomes complicated and surprising, both choose to speak (defect) and they both ends in prison for many years.

The truth is that this result is completely expected. People drowned is not altruistic and when deciding on his best interests is usually prefer himself over his partner. (Of course there are exceptions such as parents and children, good friends etc.) Mr. A and Mr. B naturally thought of personal welfare which made them decide to speak and sit in jail for years.

Experts explain the unwanted results in that both games we lack knowledge of what the other chooses.
Of course, if they could talk they would agree to keep quiet and pass the year imprisonment as mutual assistance and appreciation for the other cooperation. But when one does not know what the other chooses, he can only guess and we have already saw the result of that.

This game like many others lighten many situation in our lives, in reality.
For example, if you ask a favor from your colleague you have reasonably good chance that he would be happy to help you. It is sometimes surprising what people can do for others, stay more time at work, another effort to help a friend with their homework (even though you have already been finished), indeed, the world is beautiful.

However, when I try to cross a busy intersection every time I re surprised that people are not willing to slow their speed even for a moment and allow me to cross. The irony is, they might be exactly the same peoples, those who helped you at work, stay another hour and sacrificed leisure or rest to help you overcome the obstacle. Now, they will not even slow down and let you pass.

So what happened here anyway? How can we explain the difference in people's behavior at the different situations?

The Prisoner's Dilemma explains it this way:
When the game is iterative, it is likely that people will cooperate, but if you play once, people tend to do best for themselves.
colleague work together those it's likely that if you made a favor to someone he will be happy to return you back, after all, you see each other almost every day. Your friend knows you and you good is important to him.
However, crossing the intersection is "one time game", it is not likely to meet again the man that give or not give you a pass those the expected result will be passing by you... or as in the Prisoner's Dilemma - defects.

People cooperate (most of the time) where the game has many iterations.
When people cooperate, the world seem to be a better place.

Game Theory - Lesson 1 How to sell hundred dollars in two hundredsand 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.