more game theory quesitons

[speakerfreak]

Ok, so since the last post generated a lot of interesting discussion I thought I'd put up two other questions which I think are quite good.

A: 5 pirates find a treasure of 100 gold coins and decide to split it. They decide the following; the pirates are ranked in order of years of service, and the longest serving gets to split first. After he decided on the split a vote is taken on whether they agree (all have to vote and the pirate who splits DOES get to vote). If the vote is tied or a majority agree then the game is over but if a majority disagree the pirate is made to walk the plank and the pirate with the next longest serving record gets to split, with the pirates again voting and the same rules applying. This keeps going until a majority agree with the split, so assuming the first pirate wants to maximize his gold what split does he offer?

B: There are 15 lions in a cage and a piece of meat in the middle. The lions decide in order whether they want to eat the meat, however if they do then they fall asleep and they become the peice of meat! Assuming the lions are all perfectly logical does the first one eat the meat?

[atrifix]

A has been discussed several times before on this forum. The correct answer is something like 98, 0, 1, 1, 0.

In B, the first lion eats the meat.

[jogsxyz]

The first pirate will get nothing. It is the best interest of the other four pirates to have him walk the plank.

Same goes for the second and third pirate.

The stronger of the final two pirates will have 100 pieces of gold.

[CallMeIshmael]

[ QUOTE ]
B: There are 15 lions in a cage and a piece of meat in the middle. The lions decide in order whether they want to eat the meat, however if they do then they fall asleep and they become the peice of meat! Assuming the lions are all perfectly logical does the first one eat the meat?

[/ QUOTE ]

Question, can they go again?

Like, lets say there are only 2 lions playing the game. If the first one doesnt eat, and the second one does, does the first one get to go again and eat the second?

[CallMeIshmael]

[ QUOTE ]
The first pirate will get nothing. It is the best interest of the other four pirates to have him walk the plank.

Same goes for the second and third pirate.

The stronger of the final two pirates will have 100 pieces of gold.

[/ QUOTE ]


Im gonna go ahead and request that no one responds to this post. We've gone far enough down that road, imo.

thanks, CMI.

[surftheiop]

First off I dont know anything about game theory.
Why is this so wrong though it seems like the less the pirates there are the more each pirate could expect to recieve so dont they want the other pirates walking the plank?

[New001]

[ QUOTE ]
First off I dont know anything about game theory.
Why is this so wrong though it seems like the less the pirates there are the more each pirate could expect to recieve so dont they want the other pirates walking the plank?

[/ QUOTE ]
Search online or in this forum if you want the detailed answer, it's done with both pirates and parrots recently. If you want to work it out on your own, try working backwards. What happens when there are two pirates? Then three? Then go all the way up to five and see how it works out. The later pirates end up at the mercy of the first pirate in terms of how much they get.

[CallMeIshmael]

Jogxyz,

I will say this. I just finished a second level game theory course. The pirate problem was on the exam. The solution you presented would have gotten 0 points.

If you want to present "what I think might happen" well, thats ok. But, your solution is not correct in terms of game theory.

Here is the exam with answers (its problem 2)

http://instruct1.cit.cornell.edu/courses/econ368/exam01ans.pdf

[New001]

Slightly off topic, but what is a game theory class like? I've got a little math background (up through multivariable calc and ODE), and the game theory problems are all kinda interesting to me. I'm pretty bad at them though, but I'd love to learn more.

[surftheiop]

Ah thanks for that, that makes more sense now that i look at the answer and explanation. Although it does leave me wondering how usefull is game theory to real situations? Because im pretty sure the pirate proposing 97 for himself would get chucked overboard 999/1000 times if it came up in real life

[CallMeIshmael]

[ QUOTE ]
Slightly off topic, but what is a game theory class like?

[/ QUOTE ]

ummm... awesome?

[ QUOTE ]
I've got a little math background (up through multivariable calc and ODE), and the game theory problems are all kinda interesting to me. I'm pretty bad at them though, but I'd love to learn more.

[/ QUOTE ]


I mean, being interested in the problems is probably enough to put you at at least a B in the curve, since Ive found that people who take GT courses are naturally pretty bad at them.


If you have an interest, def. take it. Of the two Ive taken, one was more a look at psychology and listed as an arts course, while the other was pure math and listed as a math course. Personally, I preferred the former since it was REALLY interesting.

[New001]

I'll look into it, thanks.

[CallMeIshmael]

[ QUOTE ]
Ah thanks for that, that makes more sense now that i look at the answer and explanation. Although it does leave me wondering how usefull is game theory to real situations? Because im pretty sure the pirate proposing 97 for himself would get chucked overboard 999/1000 times if it came up in real life

[/ QUOTE ]

But this never comes up in real life. The situation described in the OP is completely within the theoretic realm. The solutions to GT problems are far more relevant (and accurate) when we model real life situations.

[surftheiop]

I dont know any game theory notation so the 1st and 3rd problems on the midterm mean nothing to me but are either of them actually modeling real life situations? If they are could you maybe tell me a little more about it and if they arent could you post GT applied to a real situation because most the stuff on here seems completly thoeretical.

Thanks for your replies, this stuff is interesting to me but unfortunately im not in college yet and dont take economics until the fall so i dont know much about it.

[atrifix]

[ QUOTE ]
Question, can they go again?

Like, lets say there are only 2 lions playing the game. If the first one doesnt eat, and the second one does, does the first one get to go again and eat the second?

[/ QUOTE ]

I assumed the game was infinitely repeated; it's the only thing that leads to a paradoxical solution. If it is only a one-shot game, then the trivial answer is that all lions except the last defer to the last lion.

[TomCollins]

[ QUOTE ]
The first pirate will get nothing. It is the best interest of the other four pirates to have him walk the plank.

Same goes for the second and third pirate.

The stronger of the final two pirates will have 100 pieces of gold.

[/ QUOTE ]

How many replies will this thread take as people try to convince this lughead he is wrong again? My guess is another 10 pages.

[CallMeIshmael]

[ QUOTE ]

I dont know any game theory notation so the 1st and 3rd problems on the midterm mean nothing to me but are either of them actually modeling real life situations? If they are could you maybe tell me a little more about it and if they arent could you post GT applied to a real situation because most the stuff on here seems completly thoeretical.

Thanks for your replies, this stuff is interesting to me but unfortunately im not in college yet and dont take economics until the fall so i dont know much about it.

[/ QUOTE ]

Im going to assume you saw the other thread and know about the problem presented in it.

At one point I posted this (and I actually dont think anyone responded to it)

[ QUOTE ]
lets say that there are a bunch of companies of type A, and a bunch of type B, and they are both doing what you call rational, and playing the 50:50 split at the beginning.

If some company comes in, and says "Hey guys, im type B, and im willing to take only 45". What are type A companies going to do??? Well, I would bet they would ALL go to that one company B. So, that company B now has 100% of the market, and they are making a ton.

But, what if a new company B comes in and says they'll take 30. Well, all of the A's will now go there.

Do you see where this is going?

[/ QUOTE ]



What is happening here is evolution, just like animals go through it. Game theory is most applicable when competition forces things to become extinct, since this is what pushes things towards Nash solutions.


This is why GT is so important in animal behaviour.


The only thing is, situations where GT is applicable tend to be complex. I mean, real life decisions arent as simple as the ones presented.


This paper is probably the easiest to understand of the ones I have immediate access to, but is still tough:

http://www.geocities.com/call_me_ishmael_2002/003.pdf

[CallMeIshmael]

[ QUOTE ]
[ QUOTE ]
Question, can they go again?

Like, lets say there are only 2 lions playing the game. If the first one doesnt eat, and the second one does, does the first one get to go again and eat the second?

[/ QUOTE ]

I assumed the game was infinitely repeated; it's the only thing that leads to a paradoxical solution. If it is only a one-shot game, then the trivial answer is that all lions except the last defer to the last lion.

[/ QUOTE ]


Are we also assuming that if a lion becomes meat, it is meat, it remains meat for the rest of the game? and dies when another eats? (this is what Im assuming)


Under these assumptions, if 15 eats, it means that 1-14 NEVER eat, and that 16 must not eat (if it started at 16).

With that result, 15 becomes a very special number, and Ive yet to figure out why /images/graemlins/mad.gif /images/graemlins/mad.gif /images/graemlins/mad.gif


(no clues please, lets just confirm that under the above assumptions 15 can eat)

[atrifix]

[ QUOTE ]
Are we also assuming that if a lion becomes meat, it is meat, it remains meat for the rest of the game? and dies when another eats? (this is what Im assuming)

[/ QUOTE ]

Yes, that seems reasonable. The other assumptions I made were that a lion prefers meat to nothing, but prefers going hungry to being eaten. The lions are rational and there is CKR.

[ QUOTE ]
Under these assumptions, if 15 eats, it means that 1-14 NEVER eat, and that 16 must not eat (if it started at 16).

With that result, 15 becomes a very special number, and Ive yet to figure out why /images/graemlins/mad.gif /images/graemlins/mad.gif /images/graemlins/mad.gif


(no clues please, lets just confirm that under the above assumptions 15 can eat)

[/ QUOTE ]

I don't understand this part. Can you rephrase that?

[jogsxyz]

[ QUOTE ]
Jogxyz,

I will say this. I just finished a second level game theory course. The pirate problem was on the exam. The solution you presented would have gotten 0 points.

If you want to present "what I think might happen" well, thats ok. But, your solution is not correct in terms of game theory.

Here is the exam with answers (its problem 2)

http://instruct1.cit.cornell.edu/courses/econ368/exam01ans.pdf

[/ QUOTE ]

As Andrew both you and your prof would walk the plank.
You prof does not explain why any of the others would vote in favor of this proposal.

[jogsxyz]

In It's a Mad, Mad, Mad World there was a similiar game. No one ended up with any of the money.

That's the real world.

[CallMeIshmael]

[ QUOTE ]
[ QUOTE ]
Under these assumptions, if 15 eats, it means that 1-14 NEVER eat, and that 16 must not eat (if it started at 16).

With that result, 15 becomes a very special number, and Ive yet to figure out why /images/graemlins/mad.gif /images/graemlins/mad.gif /images/graemlins/mad.gif


(no clues please, lets just confirm that under the above assumptions 15 can eat)

[/ QUOTE ]

I don't understand this part. Can you rephrase that?

[/ QUOTE ]



IF its rataional for 15 to eat (which it probably is, since a) that is what you got and b) if it werent, the problem isnt interesting) is means that:


A) the other 14 lions can never eat. If we number the lions 1-15, with 15 being the first to act, then it is only rational for 15 to eat if it is not rational for any of the following lions to eat when 15 eats.

B) If somehow we started off with 16, it would not be rational for 16 to eat, since when it does, we come to the problem in the OP, and we know that 15 rationall eats.



Any solution that has 15 eating must have the next 14 ALL not eating in an infinite loop. And I just cant see what about the number 15 makes it so special.

[CallMeIshmael]

[ QUOTE ]
As Andrew both you and your prof would walk the plank.
You prof does not explain why any of the others would vote in favor of this proposal.

[/ QUOTE ]


Very true. I cant believe I had it wrong the whole time /images/graemlins/frown.gif

[TomCollins]

[ QUOTE ]
In It's a Mad, Mad, Mad World there was a similiar game. No one ended up with any of the money.

That's the real world.

[/ QUOTE ]

Did you miss the part where it said "game theory" at the beginning? What does it have to do with the real world? I'm starting to believe you are just trolling.

[CallMeIshmael]

[ QUOTE ]
Did you miss the part where it said "game theory" at the beginning? What does it have to do with the real world? I'm starting to believe you are just the sharkey of game theory.

[/ QUOTE ]

[CallMeIshmael]

OK, there we go, got it. duh /images/graemlins/frown.gif

[bobman0330]

[ QUOTE ]
There are 15 lions in a cage and a piece of meat in the middle. The lions decide in order whether they want to eat the meat, however if they do then they fall asleep and they become the peice of meat! Assuming the lions are all perfectly logical does the first one eat the meat?

[/ QUOTE ]

Yes. Work backwards from the last lion. The penultimate lion, if he eats, will get eaten by the last lion, who doesn't have anything to worry about. So the 3rd to last lion can eat without getting devoured by penultimate lion. Etc.

[dms]

There doesn't seem to be anything special about the #15 if you're going to say that 1-14 don't eat. Until one lion eats, the situation each lion finds himself in is the same as the lion before him.

I don't think atrifix claims that #15 eats, just that #15 would eat if #1 didn't act after him.

[CallMeIshmael]

[ QUOTE ]
I don't think atrifix claims that #15 eats, just that #15 would eat if #1 didn't act after him.

[/ QUOTE ]

I dont understand what this means. Can you reword?

(FWIW, I solved it already, just had a road block about something)

[dms]

[ QUOTE ]
[ QUOTE ]
I don't think atrifix claims that #15 eats, just that #15 would eat if #1 didn't act after him.

[/ QUOTE ]

I dont understand what this means. Can you reword?

(FWIW, I solved it already, just had a road block about something)

[/ QUOTE ]

Responding to atrifix, you said:

"IF its rataional for 15 to eat (which it probably is, since a) that is what you got"

I don't think atrifix ever claimed that it's rational for 15 to eat (except under different conditions).

[CallMeIshmael]

[ QUOTE ]
Responding to atrifix, you said:

"IF its rataional for 15 to eat (which it probably is, since a) that is what you got"

I don't think atrifix ever claimed that it's rational for 15 to eat (except under different conditions).

[/ QUOTE ]



I believe that is exactly what he claimed when he said "In B, the first lion eats the meat. "


When I say "15" I mean the lion that acts with 14 other lions still ahead of him, and hence the first to act.

[dms]

haha, my bad. I didn't notice his first post, I just saw the ones in sub-thread. Something really didn't make sense...

[TomCollins]

[ QUOTE ]
[ QUOTE ]
There are 15 lions in a cage and a piece of meat in the middle. The lions decide in order whether they want to eat the meat, however if they do then they fall asleep and they become the peice of meat! Assuming the lions are all perfectly logical does the first one eat the meat?

[/ QUOTE ]

Yes. Work backwards from the last lion. The penultimate lion, if he eats, will get eaten by the last lion, who doesn't have anything to worry about. So the 3rd to last lion can eat without getting devoured by penultimate lion. Etc.

[/ QUOTE ]

He won't get devoured by the penultimate lion, but he will get eaten by the last lion. So he won't eat.

[CallMeIshmael]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
There are 15 lions in a cage and a piece of meat in the middle. The lions decide in order whether they want to eat the meat, however if they do then they fall asleep and they become the peice of meat! Assuming the lions are all perfectly logical does the first one eat the meat?

[/ QUOTE ]

Yes. Work backwards from the last lion. The penultimate lion, if he eats, will get eaten by the last lion, who doesn't have anything to worry about. So the 3rd to last lion can eat without getting devoured by penultimate lion. Etc.

[/ QUOTE ]

He won't get devoured by the penultimate lion, but he will get eaten by the last lion. So he won't eat.

[/ QUOTE ]


But you never get to the last lion, since its cyclical.


If there are 2 left, they continue to refuse to eat, since they know if they do that they die. Therefore, if n = 2, they never eat.

As such, if n = 3, the lion can safely eat.

As such, if n=4, the lion cannot eat.

Therefore, if n=5 the lion can eat.

[TomCollins]

The wording of the question is extremely unclear how the game works. After all 15 lions eat or don't eat, then they start again?

[CallMeIshmael]

[ QUOTE ]
The wording of the question is extremely unclear how the game works. After all 15 lions eat or don't eat, then they start again?

[/ QUOTE ]

We think.


I was unsure about this for a while as well.

[CallMeIshmael]

[ QUOTE ]
The first pirate will get nothing. It is the best interest of the other four pirates to have him walk the plank.

Same goes for the second and third pirate.

The stronger of the final two pirates will have 100 pieces of gold.

[/ QUOTE ]


[censored] it, I'll bite...


If the first three know they are going to walk the plank, dont you think they would agree to ANY offer in the first round?

[atrifix]

[ QUOTE ]
B) If somehow we started off with 16, it would not be rational for 16 to eat, since when it does, we come to the problem in the OP, and we know that 15 rationall eats.



Any solution that has 15 eating must have the next 14 ALL not eating in an infinite loop. And I just cant see what about the number 15 makes it so special.

[/ QUOTE ]

15 is special only in that it is odd. Any other odd number works just as well.

Clearly we agree that in the game with 1 lion, the lion eats the meat.

In the game with 2 lions, neither lion eats the meat, because to do so is suicidal.

In the game with 3 lions, the 3rd lion eats the meat, because he knows that the 2 lions ahead of him will not eat him at risk to themselves.

...and so on.

[CallMeIshmael]

[ QUOTE ]
[ QUOTE ]
B) If somehow we started off with 16, it would not be rational for 16 to eat, since when it does, we come to the problem in the OP, and we know that 15 rationall eats.



Any solution that has 15 eating must have the next 14 ALL not eating in an infinite loop. And I just cant see what about the number 15 makes it so special.

[/ QUOTE ]

15 is special only in that it is odd. Any other odd number works just as well.

Clearly we agree that in the game with 1 lion, the lion eats the meat.

In the game with 2 lions, neither lion eats the meat, because to do so is suicidal.

In the game with 3 lions, the 3rd lion eats the meat, because he knows that the 2 lions ahead of him will not eat him at risk to themselves.

...and so on.

[/ QUOTE ]

Me not knowing the solution was SOOOO 2 hours ago /images/graemlins/grin.gif /images/graemlins/grin.gif

[JMAnon]

[ QUOTE ]
The wording of the question is extremely unclear how the game works. After all 15 lions eat or don't eat, then they start again?

[/ QUOTE ]

It must be, otherwise the game would be too simple to solve. None of the lions would be able to eat, except the last lion, because they would know that the last lion would be able to eat without consequence.

[jogsxyz]

[ QUOTE ]
Ah thanks for that, that makes more sense now that i look at the answer and explanation. Although it does leave me wondering how usefull is game theory to real situations? Because im pretty sure the pirate proposing 97 for himself would get chucked overboard 999/1000 times if it came up in real life

[/ QUOTE ]

I think the Econ prof would get chucked overboard first.

[bobman0330]

[ QUOTE ]
He won't get devoured by the penultimate lion, but he will get eaten by the last lion. So he won't eat.

[/ QUOTE ]

The OP wasn't very clear. I'm pretty sure that each lion can only be eaten by the next lion. Otherwise the game is degenerate, and no lion eats. Unless it's not cyclical, in which case the last lion eats.

[atrifix]

[ QUOTE ]
But this never comes up in real life. The situation described in the OP is completely within the theoretic realm. The solutions to GT problems are far more relevant (and accurate) when we model real life situations.

[/ QUOTE ]

I disagree. IMO there are some fundamental difficulties in applying GT to real life problems that have not yet been satisfactorily resolved.

If I were ever in this situation in real life, I would almost certainly propose 20, 20, 20, 20, 20. If I thought the other pirates were collaborating against me, I might even go so far as to propose 0, 25, 25, 25, 25 (or something in between).

[CallMeIshmael]

[ QUOTE ]
If I were ever in this situation in real life, I would almost certainly propose 20, 20, 20, 20, 20. If I thought the other pirates were collaborating against me, I might even go so far as to propose 0, 25, 25, 25, 25 (or something in between).

[/ QUOTE ]



But you're never in this situation in real life.

No group of pirates (or any group of people) would split up money in this manner.

[atrifix]

[ QUOTE ]
[ QUOTE ]
If I were ever in this situation in real life, I would almost certainly propose 20, 20, 20, 20, 20. If I thought the other pirates were collaborating against me, I might even go so far as to propose 0, 25, 25, 25, 25 (or something in between).

[/ QUOTE ]



But you're never in this situation in real life.

[/ QUOTE ]

And every day, I thank God for precisely that.

[ QUOTE ]
No group of pirates (or any group of people) would split up money in this manner.

[/ QUOTE ]

I would expect an even split, more or less.