Game theory time: Lions and the Lamb

[b0rk]

Here's a fun one:

A sheep sits in the middle of a field surrounded by n lions (where n is some number greater than 10). Any lion can eat the sheep but, as each lion knows, it would become so tired that it would be as defenseless as a sheep itself--easy prey for another hungry lion who would in turn become tired and defenseless. The lions are all hungry (equally so for lamb or lion meat), super rational, but naturally not suicidal. Does the nearest lion, or any lion for that matter, pounce on the tasty ovine?

For those who enjoyed the hand shaking puzzle, here's a problem from the mid-term exam of my undergraduate Economics game-theory class...

[Tshute]

What the heck..? I vote that 1 lion eats a lamb, knowing the rest are not stupid enough to eat him.

I don't get it.

[gaurav_fhs]

Hey this applies as much to Biology and sociology as it does to economics. Game theory rocks

[b0rk]

Actually, belive it or not, I was asked this on my University of Toronto exam..I'm not surprised that not many of you will be able to figure this out as the class average was quite high so the prof had to 'play' around with our averages

It's ok not to get the 'right' answer for 'full marks' but at least you tried!

[Tshute]

Every lion will probably just give'r even with the consequences. That's my vote.

[gaurav_fhs]

Well you can include co-operativity I assume. Why should merely 1 lion attack the sheep? Or for that matter only 1 lion attack the weakest lion?

Oooh how about putting in a clause-- if a lion waits too long, it dies of hunger.

[b0rk]

Well you can include co-operativity I assume. Why should merely 1 lion attack the sheep? Or for that matter only 1 lion attack the weakest lion?

Oooh how about putting in a clause-- if a lion waits too long, it dies of hunger.

LOL, that's what many students wrote on their exam papers, and guess what? 0/10! It's encouraging to see that you're making assumptions, but making assumptions on exams will not give you 10/10

[Tshute]

LOL, that's what many students wrote on their exam papers, and guess what? 0/10! It's encouraging to see that you're making assumptions, but making assumptions on exams will not give you 10/10

I don't understand how there can be a right and wrong answer for this though. If you ran multiple experiments like this, different outcomes are bound to happen.

[b0rk]

I don't understand how there can be a right and wrong answer for this though. If you ran multiple experiments like this, different outcomes are bound to happen.

You can also apply this question to CS and ENG students, as they typically think in algorithms and are good at applying themselves to theoretical questions. My ENGSCI friend answered it in 2 mins . Go figure.

[chchchigga]

I vote that a lion goes for it - revising...if n is odd. If n is even, no one goes.
Since for an even n, i.e. 4 lions, lion 4 knows that lion 3 will go for it knowing that lion 2 won't go for it leaving lion 1 with a free meal.

[d_jedi]

Here's a fun one:



For those who enjoyed the hand shaking puzzle, here's a problem from the mid-term exam of my undergraduate Economics game-theory class...

I would say no. Each wants the other lions to eat first - such that the probability it gets eaten is less (in each case, a lion has 10 targets to choose from - but the earlier a lion chooses to eat, the more chances it has of being eaten by other lions).

Edit: By simple probability, we know the chances of getting eaten for each lion is as follows:
Lion Survival chance
1 0.387420489
2 0.43046721
3 0.4782969
4 0.531441
5 0.59049
6 0.6561
7 0.729
8 0.81
9 0.9
10 1

So it is advantageous for each lion to wait. Hence, no lion eats, hoping the others will do so before.

[gaurav_fhs]

OK seeing how all the lions are super rational and not suicidal (and yet donot want to co-operate), I'd say they all starve to death.

Although I'm pretty sure, I'm missing a link

PS: I'm assuming in chchchigga's case, one lion will eat the lion that ate the sheep hoping the others wont eat him and so on...until the last lion (most patient dude) remains.

[Tshute]

I say the lions ignore the sheep and just turn on each other right away (although in nature this would NEVER happen).

[ainsane]

I took game theory too Great course... except most people had no idea what was going on.

I'll let others take a stab at it.

[Mems]

Hmm, I'm only 16 so don't laugh at my answer.

I believe that a lion will go for it.

-Mems