Game Theory

What is the basis for reason? And mathematics?

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duszek
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Game Theory

Post by duszek » Wed May 11, 2016 1:07 pm

Two thieves are captured and they have the following options:

If they both remain silent they will both get a 1 year sentence.
If they both speak and confess they will both get a 2 year sentence.
If one of the two confesses and the other one remains silent the confessing one will go free (Kronzeuge) and the other one will get a 3 year sentence.

The two cannot make arrangements with each other.
What is the most reasonable for them to do ? To speak or to confess ?

One of them thinks:

assuming the other one speaks then it is better for me to speak too, otherwise I will get 3 years
assuming the other one remains silent then I can go free if I speak

In both cases it is better for me to speak.

The other one thinks in the same way.

So they both speak and they both get a 2 years sentence.

Whereas if they both remained silent they would both get a 1 year sentence.

Strange, isn´t it ?

P.S. I am not sure if the official criminal law is not distorted in this case but this can be some private criminal law, created for the sake of illustrating the issue.

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Bill Wiltrack
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Re: Game Theory

Post by Bill Wiltrack » Sat Oct 22, 2016 9:16 am

.




I'm SURE this exercise makes sense in your mind but because it's totally theoretical and rather ambiguous, over 150 hits tells you no one here cares...






.

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TSBU
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Re: Game Theory

Post by TSBU » Sat Oct 22, 2016 10:00 am

duszek wrote: Strange, isn´t it ?
Why?

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TSBU
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Re: Game Theory

Post by TSBU » Sat Oct 22, 2016 10:09 am

Dos sabios fueron capturados por un tirano rey y hechos prisioneros.
Para poner a prueba su inteligencia fueron encerrados en celdas separadas de una torre, una que miraba hacia el Este y otra hacia el Oeste, y de modo que no pudieran comunicarse entre sí.
Desde sus celdas ellos podían ver, entre ambos, todas las ciudades que componían el reino, pero ninguna ciudad era visible a la vez por los dos.
El tirano les dijo que las ciudades del reino eran o bien 10 o bien 13, y que ambos serían liberados tan pronto como uno cualquiera de ellos pudiera anunciarle al carcelero, que cada mañana les llevaba la comida, cuántas ciudades integraban el reino.
En la quinta mañana, los dos sabios fueron liberados.

¿Qué proceso lógico les llevó a resolver su problema?. ¿Cuántas ciudades componen el reino?. ¿Cuántas ciudades vio cada uno?

Two inteligent men were captured by a mad k... by a king.
He put them in a tower, in different locked cells (they can't comunicate), one with a window to the East, and one with a window to the West.
They could see all the citys in the kingdom, but none of the citys could be seen for both of them at the same time.

The king told them that the numer of citys were 10, or 13. He said that they both were going to be free as soon as one of them could tell how many citys were there. Every day, the jailer asked both men if they have the answer.

The fifth day, they are released.

How many cities were there?

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Terrapin Station
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Re: Game Theory

Post by Terrapin Station » Sat Oct 22, 2016 1:12 pm

Game theory is wonky in that it assumes "ideal rational agents" and people are not that. That's a problem with a lot of online interaction, too. People assume "ideal rational agent" about themselves, too, when that's not warranted.

It really depends on the people involved. Ideally, you know something about the other people, so that you can make predictions based on that knowledge.

If you don't know the other people, you're always gambling on factors that there's no way to predict. Is the other person a sociopath? How well are they able to reason and to what extent might that countervene stubborn psychological factors? Etc. You're dealing with individuals and they have individual psychological quirks, different abilities, etc.

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TSBU
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Re: Game Theory

Post by TSBU » Sat Oct 22, 2016 4:55 pm

Terrapin Station wrote:Game theory is wonky in that it assumes "ideal rational agents" and people are not that. That's a problem with a lot of online interaction, too. People assume "ideal rational agent" about themselves, too, when that's not warranted.

It really depends on the people involved. Ideally, you know something about the other people, so that you can make predictions based on that knowledge.

If you don't know the other people, you're always gambling on factors that there's no way to predict. Is the other person a sociopath? How well are they able to reason and to what extent might that countervene stubborn psychological factors? Etc. You're dealing with individuals and they have individual psychological quirks, different abilities, etc.
No. Game theory is language for mathematicians, it serve a purpose: express problems. Chek it out in wikipedia. Your concept about "ideal rational agents" I don't like it very much XD.

Also, I put a logic game, solve it and I'll give you a present (but I don't know if you would like it, I guess you would like it XD).

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Terrapin Station
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Re: Game Theory

Post by Terrapin Station » Sat Oct 22, 2016 6:20 pm

TSBU wrote:No. Game theory is language for mathematicians,
It's not that I'm not familiar with game theory. I'm critiquing the assumptions it makes.

That those assumptions are problematic doesn't mean that it can't have instrumental, upshot value for some practical/applied uses.

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Arising_uk
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Re: Game Theory

Post by Arising_uk » Sun Oct 23, 2016 2:07 am

TSBU wrote:...

Two inteligent men were captured by a mad k... by a king.
He put them in a tower, in different locked cells (they can't comunicate), one with a window to the East, and one with a window to the West.
They could see all the citys in the kingdom, but none of the citys could be seen for both of them at the same time.

The king told them that the numer of citys were 10, or 13. He said that they both were going to be free as soon as one of them could tell how many citys were there. Every day, the jailer asked both men if they have the answer.

The fifth day, they are released.

How many cities were there?
Sorry but I don't understand this, is it translated correctly? As the King has said there are 10 or 13 cities so in the worst case they should have been released by the second day, as say there were 10 cities and both on the first day said 13 then no release but the next day one would say 10 and they'd be released otherwise they'd have been released on the first day as one would have said 10. So how did you get to five days?

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Arising_uk
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Re: Game Theory

Post by Arising_uk » Sun Oct 23, 2016 2:11 am

If you'd like to explore game theory, morals, philosophy and 'AI' and you like logic and declarative programming, e.g. Prolog, then this is the book for you - https://www.amazon.co.uk/Artificial-Mor ... 0415034841

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TSBU
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Re: Game Theory

Post by TSBU » Sun Oct 23, 2016 8:39 am

Arising_uk wrote:
TSBU wrote:...

Two inteligent men were captured by a mad k... by a king.
He put them in a tower, in different locked cells (they can't comunicate), one with a window to the East, and one with a window to the West.
They could see all the citys in the kingdom, but none of the citys could be seen for both of them at the same time.

The king told them that the numer of citys were 10, or 13. He said that they both were going to be free as soon as one of them could tell how many citys were there. Every day, the jailer asked both men if they have the answer.

The fifth day, they are released.

How many cities were there?
Sorry but I don't understand this, is it translated correctly? As the King has said there are 10 or 13 cities so in the worst case they should have been released by the second day, as say there were 10 cities and both on the first day said 13 then no release but the next day one would say 10 and they'd be released otherwise they'd have been released on the first day as one would have said 10. So how did you get to five days?
They can't do mistakes. If they fail with the first answer, they die. It has an answer, a logical one, with no cheats or tricks of any kind.

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Arising_uk
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Re: Game Theory

Post by Arising_uk » Sun Oct 23, 2016 9:54 am

TSBU wrote:...

They can't do mistakes. If they fail with the first answer, they die. It has an answer, a logical one, with no cheats or tricks of any kind.
Sorry still don't understand, if they die if they make mistakes how did they get to day five?

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TSBU
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Re: Game Theory

Post by TSBU » Sun Oct 23, 2016 10:07 am

Arising_uk wrote:
TSBU wrote:...

They can't do mistakes. If they fail with the first answer, they die. It has an answer, a logical one, with no cheats or tricks of any kind.
Sorry still don't understand, if they die if they make mistakes how did they get to day five?
Without mistakes -.-

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Arising_uk
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Re: Game Theory

Post by Arising_uk » Sun Oct 23, 2016 10:52 am

TSBU wrote:Without mistakes -.-
Then they would have been released on day one?

I'm not saying this isn't a puzzle just that I think something has been lost in the translation?

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Terrapin Station
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Re: Game Theory

Post by Terrapin Station » Sun Oct 23, 2016 12:42 pm

Arising_uk wrote:
TSBU wrote:Without mistakes -.-
Then they would have been released on day one?

I'm not saying this isn't a puzzle just that I think something has been lost in the translation?
Yeah, it doesn't make sense to me either. My first assumption was, "Well, the king could be lying." The problem is that in that case, there's not enough information to solve it beyond the prisoners making random guesses, but that doesn't work for them getting out in five days.

If (a) the king isn't lying and (b) only one of the prisoners has to get the answer right, then obviously the prisoners will be out in one or two days. Two only if they both make the same, incorrect guess on day one.

If they die just in case one makes a mistake, then either they get out on day one or they did on day one, obviously.

Maybe the idea is that they both have to get the answer right. But there's still no way to make the answer definitely five days with the info given.

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TSBU
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Re: Game Theory

Post by TSBU » Sun Oct 23, 2016 12:51 pm

If one of them give a proper answer, they are both released, if one of them fail, both of them are killed. Maybe thats something that shouldbe said.

There is enough information, the king is not lying, and there are no tricks, they cant comunicate etc.

Of course, they can stay in their cells forever if they never answer.

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