Re: The Sopranos and Game Theory

#21
turangawaewae wrote:Except for this one, there is a definitive answer.
Most people will respond as you have, but you still need to think in terms of the other persons response.

If prisoner 2 confesses, you have two options. Confess, and get 8 years, don't confess, and get 10 years jail time (because prisoner 2 will turn star witness). So if prisoner 2 confesses, your optimal outcome is to confess.
If prisoner 2 doesn't confess, you have two options. Don't confess, and you get 1 year, confess and you get no jail time as you turn star witness. If prisoner 2 doesn't confess, your optimal strategy is to confess.

So no matter what prisoner 2 does, your optimal strategy is to confess!!
You're right, prisoner 2 faces the same chioces. So if both players play their optimal outcome, both confess, and they both do 8 years. Police actually use this technique in real life. Of course, you would both have been better off if you had both not confessed. You could both collude, and make a pact to not confess. But if the other prisoner is not confessing, you have an incentive to confess and do no time, rather than serving a year in prison. Thats why pacts or cartel are inherently unstable.

Of course, this is set up where jail time is the only cost. That is when I bring in the sopranos during lecture. I explain what I have just explained above, then say how would the outcomes differ if you were prisoner one and Tony Soprano was prisoner 2. Unless you want to end up under a concrete slab somewhere, you don't confess. That is because Tony is what we call a credible threat. If you make a deal to collude and both not confess, you know that you are dead if you do confess, which make not confessing and doing one year more attractive than confessing and doing no time. Of course, once Tony knows you are not confessing, he could confess, do no time, and you do 10 years!! So even with the credible threat of Tony, it may still be optimal to confess.

All of this assumes that Prisoner 2 makes a decision or confesses first. That information was not supplied. Or was it?

Re: The Sopranos and Game Theory

#22
badabellisima wrote:Oh!- You didn't mention that the other prisoner would get to have knowledge of the other prisoner's confession or lack of one. i thought they were separated in two rooms and were making isolated, independant and final decisions without knowledge of the other's position.

This so like the Lady or Tiger Tale! You economists have got me hooked. Now i am regretting not hanging in there with it in college. But i was so unable to get it- just like now! Except for some reason i am now motivated to understand.


Neither prisoner has a knowledge of what the other is doing.

Remember, game theory is about what you EXPECT the other will do. When prisoner 1 is in the interrogation room, he works out what his optimal outcome is (remember, it doesn't matter what prisoner 2 does, prisoner one's optimal strategy is to confess). Prisoner one knows prisoner two faces the same optimal outcome to confess. There is no communication between the two.

Re: The Sopranos and Game Theory

#23
And now that i read about the Tony being a 'credible threat' aspect of it- it really is a useful theory! And it truly sheds light on their thought process- how they would apply the mobster version of Game Theory to their daily lives. This is making me re-think alot of things about strategy in this show.

Re: The Sopranos and Game Theory

#24
turangawaewae wrote:Neither prisoner has a knowledge of what the other is doing.

Remember, game theory is about what you EXPECT the other will do. When prisoner 1 is in the interrogation room, he works out what his optimal outcome is (remember, it doesn't matter what prisoner 2 does, prisoner one's optimal strategy is to confess). Prisoner one knows prisoner two faces the same optimal outcome to confess. There is no communication between the two.

but each prisoner's decision strategy is based upon the other making the decision first. It is essentially a reaction to another's probable choice, in a certain order. What theory applies if you make a choice NOT based upon what the other would probably do? i mean, why consider the other at all if there's no 'credible threat' like in Mobster Game Theory? I'll check out ur answer tomorrow because i have to get up at 5am for my commute to get into The City !

Re: The Sopranos and Game Theory

#25
badabellisima wrote:but each prisoner's decision strategy is based upon the other making the decision first. It is essentially a reaction to another's probable choice, in a certain order. What theory applies if you make a choice NOT based upon what the other would probably do? i mean, why consider the other at all if there's no 'credible threat' like in Mobster Game Theory?


This is hard to explain in this form!!

Game theory is making decisions based on what you EXPECT the other parties response to be.

If you made a response NOT based on how you expect the other party will react, how would you make your decision, given that the length of your jail term depends on how the other party will react??

Here is a wikipedia link, but it gets a little complicated. I'm trying to give you the simplified version.

http://en.wikipedia.org/wiki/Prisoner's_dilemma

Re: The Sopranos and Game Theory

#26
badabellisima wrote:but each prisoner's decision strategy is based upon the other making the decision first. It is essentially a reaction to another's probable choice, in a certain order. What theory applies if you make a choice NOT based upon what the other would probably do? i mean, why consider the other at all if there's no 'credible threat' like in Mobster Game Theory? I'll check out ur answer tomorrow because i have to get up at 5am for my commute to get into The City !


Order is unimportant. You are making a decision based on what you EXPECT the other prisoner will do, not what they ACTUALLY do. Game theory is all about EXPECTED responses.

Remember with Vito, members of Tony's crew were worried about how it would LOOK if they didn't kill him or hand him over. In other words, a weak response means Phil's crew may EXPECT a weak response to other situations in the future. It's a bit like the nuclear weapon argument. You know Russia, has a nuke, so you don't fire first. If you suspect they don't you may be more inclined to nuke them. So a strong response illicits fewer attacks in the future, because the other party EXPECTS strong responses.

Re: The Sopranos and Game Theory

#27
Bada
You have given me a sleepless night. I am troubled that I have turned you off economics with an inadequate explanation of game theory, so I have called in a big gun. It is midnight, and I am currently reading chapter two of a good book called The Logic of Life By Tim Harford. He has also written another good book called The Undercover Economist. Both of them deal with economics in a way that a non-graduate in economics can understand, and both are available on Amazon. Chapter two of the logic of life deals with game theory. The king of Game Theory was an economist/mathematician called John Von Neumann. The man is immortal in the field of economics. My colleagues who have never met him recount stories of his legend. He helped to develop both the computer and the atomic bomb. In the late 1920's he developed game theory to work out the correct way to play poker. To quote Harford, Von Neumann believed that if you wanted a theory that could explain life, you should start with a theory that could explain poker!! He stated "Real life consists of bluffing, of little tactics of deception, of asking yourself what is the other man going to think I mean to do. And that is what games are about in my theory".

To show you how good Von Neumann was, to quote Harford:

"At Princeton after the war, he helped to design the fastest computer in the world, before challenging it to a calculation contest and demonstrating that he was faster. On another occasion he refused a request to assist with a new supercomputer aimed at solving an important problem, instead furnishing an immediate solution with pencil and paper. Although there were those that delved deeper, nobody was as quick as Johnny. In the popular imagination of the 1940's and 1950's, Von Neumann arguably outshined even his Princeton contemporary, Albert Einstein".

If you are interested in Game Theory, I suggest you get the Logic of Life, and read about Von Neumann's game theory development as it related to poker. But you can imagine in poker, you often have to make decisions based on what you THINK the other players are doing. If he raised, does he have a strong hand, or is he bluffing??

Just as the Lady and the Tiger has survived decades without a definitive solution, game theory has withstood the test of time (and it was created by one of the most brilliant minds to have walked the planet). I am frustrated that I have not been able to share with you the essence of the Prisoners Dilemma. Trust me, Prisoners Dilemma is not "wrong" or just simple decision making based on what another party decides. If you think that, it is because I have not explained it well, so I will attempt to explain it quickly again now!! (It is currently 12.30am!!).

Prisoners 1 and 2 don't communicate with each other, and they don't know what the other has chosen. They just have to make a choice based on what they THINK the other will do. Timing is unimportant so long as the prisoners don't find out what the other has chosen (which is why they are in separate rooms). So literally, the officers offer them both the same deal. One may say guilty straight away, but the other prisoner doesn't know this. The other prisoner may take a further day before they make their decision. He is still making a decision based on what he thinks the other prisoner will do, even though the other prisoner has already made his decision to the police.

Lets pretend that you are prisoner 1, and I am prisoner 2. We are in seperate rooms. We have both been offered the deal, if you plead guilty, and I plead not guilty, you can turn star witness and serve no time, while I get 10 years. The same deal is offered to me. Both pleading guilty means 8 years each. Both not guilty give one year each.
I am in the other room. The police officer has just outlined the information to you and I. We will not be told each others decision until we have both pled.

What do you plead? Guilty or not guilty and why?

I will outline the solution in the next slide.

Re: The Sopranos and Game Theory

#28
I will plead guilty. It actually doesn't matter to my decision what you plead.
If you go not guilty, I can plead not guilty and get 1 year, or plead guilty and do no time. I'm pleading guilty if you plead not guilty.
If you go guilty, I get 10 years by going not guilty, as you will turn star witness. If I go guilty, I only get 8 years. Going guilty when you go guilty is my optimal response.

I don't know what you have pled, but I go guilty, because that is my best response no matter what you plead.

We both face the same choice. If we both play our optimal stategy, we both go guilty and get 8 years each, which is why the police use this strategy!! However, we would both be better off if we colluded in some way, both went not guilty, and we both got one year. The problem is individual incentives. If I make a deal with you, and convince you to go not guilty before we are seperated and interegated, I have an incentive to double cross you and go guilty, and serve no jail time.

This is where the Tony Soprano credible threat is important, but prisoners dilemma assumes no credible threat to make me collude with you.

Prisoners Dilemma is a certain type of "game" where the optimal strategy results in both parties being worse off then if they had colluded.

In the Sopranos, the NJ and NY crews had what we call a repeated game. They faced many "games" with each other, so the process of working out what you THINK the other party will do can be affected by past decisions.

It is also not often the case where you get the prisoners dilemma situation, where your decision has no bearing on my optimal decision. Often I have to predict your response, and make a decsion based on that prediction, like in poker. I see your 10, and I raise you 20 Bada. Do you want to call? Do you want to fold? Do you want to reraise? What do you base your response on? You base it on what hand you THINK I have. That will be determined by how I have played previous hands (the repeat game like in the Sopranos). Have I played many hands in the past, or have I mainly folded? Have I bluffed much? Maybe if it is the first hand we have played, you will be looking for beads of sweat on my forehead, or nervous ticks. All of this is information gathering so you can make a decision based on what you THINK I have. Once you have worked out what you think I have, you work out your optimal strategy.

It really is fascinating stuff!!

Re: The Sopranos and Game Theory

#29
One things for sure- i am not at all turned off by economics or anything else in your posts! - just the opposite. With my new job, i just have a limited posting schedule 4 days a week since i get up so early and work a very long day so i can have Fridays off. So i am going to peruse all the cool stuff you just posted and jump back on this tomorrow!

Re: The Sopranos and Game Theory

#30
er, its now 'tomorrow', and i'll have to post uh, tomorrow! sorry- but its so late in Cali. Actually talked about Game theory with my Economist boss as we were trying to strategize how to deal with a problem client. He gave me a huge smile and i felt like a million bucks! Its actually helping me on my job! :icon_biggrin:
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