Here is an interesting experiment.
Background: Imagine that we are in a forest and there are N tigers roaming around. They have not eaten anything for the last 10 days and are very hungry. As a rule they will eat any meat except their own. Let us assume that rabbits are popular food among the tigers.
Constraint: If a tiger eats a rabbit, it will be automatically convert into a rabbit. Now it is fair game to other tigers. The tigers are aware of this constraint and will act rationally. Self preservation is more important than satisfying immediate hunger (thanks to Mano for pointing this out).
Scenario: One rabbit accidentally enters the area where the tigers are prowling.
Question: Will the rabbit ever be eaten? If yes what would be the general condition under which the rabbit is likely to be eaten or not?
Wednesday, August 29, 2007
Food for thought
Posted by Mad Max at 12:19 PM
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9 comments:
@madmax: doubt! Are the tigers aware of the constraint? that if they eat a rabbit- they turn into one.
@ Manohar: yes the tigers are aware of the constraint. I will add that to the main blog.
to me, it seems like the weakest tiger might be the most prone to kill the rabbit first... because, at that point, it knows it is anyway going to die and its hunger might take over... This pattern will follow till the strongest tiger in the group will survive... Survival of fittest..:)
Well, in my previous comment, when I said that the strongest tiger, I meant the rabbit from the strongest tiger...;)...before any of u get me on that...
my above comment implicitly assumed that the weakest tiger can still chase the rabbit... however, if that's not the case, and assuming that the tigers are hungry enough that they want to eat irrespective of the consequences, then, the fastest tiger will eat the rabbit and turn into a rabbit and so on till one or more of the weaker tiger(s) cannot chase the rabbit anymore and die...
If I am the stronger tiger, I will kill the rabbit. But, not eat it. Keep the dead rabbit in a cave and let it serve as a carrot for the other tigers to come and eat and turn into rabbits who are under control in the cave's confinement...
Or, kill the rabbit and cook a dish and market it to other tigers as if were a different food and serve it to everyone and turn them all into rabbits... That way, one doesnt have to wait for all the set of events to take place...All in one shot..:)
Yesterday, I was talking to Shoba about it.. She had an out-of-box thought on this...
She said, why not all the tigers share the rabbit so that all of them will turn into rabbits and they live happily ever after !!!
Question is very thought provoking. And real interesting solution from Shoba.
I think Suresh's thought process (Strong survives at the end) makes natural sense.
Rabbit on the other hand can safe guard itself by going near stronger looking Tiger with other tigers in view so that it will not dare to come closer to it.
Eventually it can out-run a weakest strong tiger. (I assume Rabbit is getting fed well :) )
@ Mindframes, survivor and brainwaves: Interesting thoughts. I like the idea of keeping it and if everybody shares then all will turn into rabbits and live happily ever after. Makes terrific sense. But the problem is the tigers act rationally. If we apply that then each tiger is trying to maximize his personal benefit and will not want to share his spoils. Therefore a joint solution will never work. Also, I think i make an error in writing the problem up. My thinking was if the rabbit is killed, then the tiger will eat it but as Mindframes correctly points out, it is possible to kill and not eat. Hence a slight rephrase, killing a rabbit implies the tiger will convert to a rabbit.
Therefore the real question is, whether you need an optimal (N) number of tigers to ensure that the rabbit is not killed or killed. If yes what would that number be.
On a first hunch, I should say that if there was just 1 tiger and 1 rabbit, it is possible that the rabbit wont be killed...may be? Also, if a rabbit (transformation of tiger) stays at the end, does it mean that the tiger survived or the rabbit?
The act of killing is a little questionable as well. For example, what if the tigers corner the rabbit and make it jump from a steep cliff (just like how villains in tamil movies do..;)). Does that imply that they killed the rabbit or not? OR trap the rabbit in a place for it to starve and die a natural death?
Also, is it correct to assume that that rabbit alone will turn the tigers into rabbit? In that case, the tigers can secretly follow the rabbit to its place where there could be other rabbits which dont follow the same rule...:)
OR, the gruesome solution:: dont kill the rabbit entirely. Just hurt it and tear of one of its organ or something and use it as a bait to attract other animals which will kill the rabbit not knowing that they will turn into a rabbit...And then, kill the transformed rabbit...
Question: If a tiger eats "a" rabbit, it will be automatically convert into a rabbit. Now it is fair game to other tigers.
Assuming they share as per Survivor, each tiger eats only a part of, as opposed to the whole rabbit as implied by the question.
So, the general condition in which the rabbit is likely to be eaten is when the tigers have understood the constraint verbatim?
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