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knowtorious
Topic Author
Posts: 49
Joined: March 18th, 2004, 4:55 pm

### the tigers and the deer

Here's a neat little puzzle:There are 99 tigers and one deer stranded on the proverbial island covered in grass.All the animals are quite happy to be eating the grass that is continually replenished, but each tiger would much rather eat the deer. Only one tiger is permitted to eat the deer (i.e. no sharing), but the catch is that the predatory tiger turns into a deer once it has eaten the original deer. The question is whether the original deer gets eaten or not and whether your answerwoul d change for a diffenerent number of tigers.

FV
Posts: 92
Joined: December 25th, 2003, 1:42 am

### the tigers and the deer

QuoteOriginally posted by: knowtoriousHere's a neat little puzzle:There are 99 tigers and one deer stranded on the proverbial island covered in grass.All the animals are quite happy to be eating the grass that is continually replenished, but each tiger would much rather eat the deer. Only one tiger is permitted to eat the deer (i.e. no sharing), but the catch is that the predatory tiger turns into a deer once it has eaten the original deer. The question is whether the original deer gets eaten or not and whether your answerwoul d change for a diffenerent number of tigers.a) If you have 1 tiger and 1 deer then the tiger definately eats the dear.b) If you have 2 tigers and 1 deer then the deer is not eaten otherwise the tiger who ate the deer who is now a deer himself gets eaten.c) With 3 tigers you are safe to eat the deer since then you are in case b.So n is odd you eat the deer. n even you do not eat the deer.

ScilabGuru
Posts: 297
Joined: October 16th, 2001, 2:14 pm

### the tigers and the deer

QuoteOriginally posted by: FVQuoteOriginally posted by: knowtoriousHere's a neat little puzzle:There are 99 tigers and one deer stranded on the proverbial island covered in grass.All the animals are quite happy to be eating the grass that is continually replenished, but each tiger would much rather eat the deer. Only one tiger is permitted to eat the deer (i.e. no sharing), but the catch is that the predatory tiger turns into a deer once it has eaten the original deer. The question is whether the original deer gets eaten or not and whether your answerwoul d change for a diffenerent number of tigers.a) If you have 1 tiger and 1 deer then the tiger definately eats the dear.b) If you have 2 tigers and 1 deer then the deer is not eaten otherwise the tiger who ate the deer who is now a deer himself gets eaten.c) With 3 tigers you are safe to eat the deer since then you are in case b.So n is odd you eat the deer. n even you do not eat the deer.Just finished the same logic. Completely agree.
Last edited by ScilabGuru on July 11th, 2004, 10:00 pm, edited 1 time in total.

exotiq
Posts: 1888
Joined: October 13th, 2003, 3:45 pm

### the tigers and the deer

Of course this all assumes that tigers are rational and both know/believe they will become what they eat and will think through the logical consequences. Many people here would probably say those two assumptions don't even apply to market participants.

Filich
Posts: 10
Joined: July 8th, 2004, 9:25 pm

### the tigers and the deer

Guys, the answer(s) given here are wrong. Do not forget, that tigers do not want to get eaten, as soon as they turn into deer. So, it is a classical problem on finding a sub-game perfect Nash equilibrium and it is often given in Oxford as an MPhil in Economics puzzle to crack in class. I won't provide you with the answer as yet, but see if you can find it yourselves.

genieman17
Posts: 27
Joined: July 16th, 2004, 4:26 pm

### the tigers and the deer

So does this mean that either one of two things will happen?1) the deer will never get eaten because the one tiger that eats him first knows that he will then get eaten, so no one tiger will try to eat him.2) the deer will never get eaten because the tigers will all fight over the one deer killing eachother off. I dunno...

Ouyang
Posts: 100
Joined: January 17th, 2002, 5:42 am

### the tigers and the deer

genieman17
Posts: 27
Joined: July 16th, 2004, 4:26 pm

### the tigers and the deer

Quotea) If you have 1 tiger and 1 deer then the tiger definately eats the dear.b) If you have 2 tigers and 1 deer then the deer is not eaten otherwise the tiger who ate the deer who is now a deer himself gets eaten.c) With 3 tigers you are safe to eat the deer since then you are in case b.So n is odd you eat the deer. n even you do not eat the deer.I have a question about this theory...at 3 tigers you are safe to eat the deer because with 2 tigers remaining, neither will eat it for fear of being eaten himself. If we creade a "d" scenario with 4 tigers, then the deer will not be eaten because then you have case c in which you will get eaten also. So the answer is that at 99 tigers, the deer will get eaten, however it will not progress past 98 tigers because at even numbers of tigers the deer doesn't get eaten?
Last edited by genieman17 on July 22nd, 2004, 10:00 pm, edited 1 time in total.

tristanreid
Posts: 441
Joined: May 12th, 2004, 6:58 pm

### the tigers and the deer

QuoteOriginally posted by: genieman17Quotea) If you have 1 tiger and 1 deer then the tiger definately eats the dear.b) If you have 2 tigers and 1 deer then the deer is not eaten otherwise the tiger who ate the deer who is now a deer himself gets eaten.c) With 3 tigers you are safe to eat the deer since then you are in case b.So n is odd you eat the deer. n even you do not eat the deer.I have a question about this theory...at 3 tigers you are safe to eat the deer because with 2 tigers remaining, neither will eat it for fear of being eaten himself. If we creade a "d" scenario with 4 tigers, then the deer will not be eaten because then you have case c in which you will get eaten also. So the answer is that at 99 tigers, the deer will get eaten, however it will not progress past 98 tigers because at even numbers of tigers the deer doesn't get eaten?Correct. The deer will get eaten, the tiger will turn into a deer, and then the system will be in stasis.-t.

beatarmy96
Posts: 12
Joined: March 17th, 2004, 4:38 pm

### the tigers and the deer

I respectfully disagree with the answer that an odd number of tigers means the deer will get eaten while an even number means it will not. If there an even number of tigers (n>2), then the rationale provided for eating the deer still holds. The only reason not to eat the deer is that you will get eaten yourself but every participant shares that position so the deer could be eaten but the question now becomes how do we, as the tigers we are, decide who eats that tasty lil deer. I propose that it is a Nash equilibrium with n>2 that the deer not be eaten at all with all tigers deciding to eat grass and survive rather than eat deer and die. That does of course assume that the utility function of surviving puts survival over the experience of eating the deer (probably rational). The best way to envision the problem I think is to put yourself in the place of the tiger that is about to eat the deer. What do you do? This does all assume, by the way, that participants have perfect information but if the island is small enough, it might not be a bad assumption. Another question would be, what if the tigers didn't know they would turn into a deer until the first tiger ate the deer? Does that change things? (hint: again, how do we choose who eats the deer the first time as we all want it)

alexandreC
Posts: 678
Joined: June 9th, 2004, 11:35 pm

### the tigers and the deer

QuoteOriginally posted by: beatarmy96how do we, as the tigers we are, decide who eats that tasty lil deer.I propose that [...] the deer not be eaten at all with all tigers deciding to eat grass and survive rather than eat deer and die. I also respectfuly disagree, this time with your opinion.If you and your friend found a 50 quid bill in the street (1),I reckon that you would not be able to decide who would keep the money, so, you might just as well leave the bill in the same place, no?Alex(that made me remember some Physics models where symmetry breakings are present.) (1)imagine that you cant devide the money cos he is flying to south america or something.
Last edited by alexandreC on August 2nd, 2004, 10:00 pm, edited 1 time in total.

Baltazar
Posts: 37
Joined: January 21st, 2004, 4:27 pm

### the tigers and the deer

I'd say, if the game is: "you can take the money but then you die and your murderer takes the money" wichih is, i think, a correct analogy with the tiger game,yeh, the note will stay on the pavement, exept if I'm alone (one tiger), i take the note and i'm happy B.

alexandreC
Posts: 678
Joined: June 9th, 2004, 11:35 pm

### the tigers and the deer

QuoteOriginally posted by: BaltazarI'd say, if the game is: "you can take the money but then you die and your murderer takes the money" wichih is, i think, a correct analogy with the tiger game,yeh, the note will stay on the pavement, exept if I'm alone (one tiger), i take the note and i'm happy B.well, if you, a tiger like you, tiger me,and a yummi yummi deer,are in an island,then I think I will eat the yummmi yummi deer,whereas you and your friend just watch!sounds good to me! Alex
Last edited by alexandreC on August 2nd, 2004, 10:00 pm, edited 1 time in total.

Ouyang
Posts: 100
Joined: January 17th, 2002, 5:42 am

### the tigers and the deer

QuoteOriginally posted by: alexandreCwell, if you, a tiger like you, me and a dear are in an island,I will eat the yummmi yummi dear,and you and your friend will watch! sounds good to me!AlexWhy in the world would any tiger want to become a deer? Someone said he would never eat the deer as long as he would not die without eating the deer. I accept this answer as correct. Someone went even further as saying he would eat a tiger instead of eating a deer. If tigers are cannibal , I think this answer is also correct. I believe we can add some incentives for tigers to eat the deer. Something like after eating the deer and suriviving for certain days the tiger will change back into a tiger and become the tiger king.

alexandreC
Posts: 678
Joined: June 9th, 2004, 11:35 pm

### the tigers and the deer

Ouyang,right!... fair enough! (maybe with this little extra incentive of yours, baltazar and beatarmy96 will change their minds!)Alex
Last edited by alexandreC on August 2nd, 2004, 10:00 pm, edited 1 time in total.

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