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Guess Number play

Joined
11/29/11
Messages
59
Points
18
Suppose there are 100 people in the classroom. A teacher comes in and asks each one to write down a number between 0 and 100 such that a person who states a number close to 2/3 of the maximum of all stated numbers wins. Which number would you choose if you were one of them?
 
Depends on the location of classroom , I would choose zero if its a harvard or a yale classroom
 
Suppose there are 100 people in the classroom. A teacher comes in and asks each one to write down a number between 0 and 100 such that a person who states a number close to 2/3 of the maximum of all stated numbers wins. Which number would you choose if you were one of them?

Stanford Game Theory Lab?
 
Well, 0 can't be the best choice. If everyone else chooses 0, then the person who chooses anything >= 1 wins.
 
Well, 0 can't be the best choice. If everyone else chooses 0, then the person who chooses anything >= 1 wins.
What if everyone chooses zero, every one wins... Governing dynamics, John Nash
"Best result comes when everyone in the group does what's best for himself and the group" :)
 
What if everyone chooses zero, every one wins... Governing dynamics, John Nash
"Best result comes when everyone in the group does what's best for himself and the group" :)
Naw, 1 seems to strictly dominate 0. I mean 2/3 of 1 is closer to 1 than 0. I can see a case where 50 is better than 80 (and vice versa), but not a case where 0 is a better choice than 1.
 
yes... But I come from School of divinity.... Best result for all :p
If its 1, I win , If its 0 everyone wins...
 
In my opinion, if we consider this as a total stochastic process, the probability of no one choosing 100 is quite low, and 67 is definitely the best choice.
But actually, 100 is not really big enough, so maybe 67 is the best choice when there are 100000 or more people.

On the other hand, if the best choice does exist, I highly doubt that there is any better strategies than choosing 1. Suppose the best choice is X, and I'm sitting in the classroom of Harvard or MIT where everyone else is just too clever not to choose X, then the best choice in this particular case becomes X*2/3. Only if X=0 or 1 will this contradiction be resolved, and as stated above, 1 is better than 0.

Guessing only, anyone has better ideas?
 
yes... But I come from School of divinity.... Best result for all :p
If its 1, I win , If its 0 everyone wins...
Everyone can also win if everyone chooses 1, but you can also lose if you choose 1 and everyone else chooses 0. If it is a random choice between 0 and 1, it seems 0 would still be the best choice
 
Everyone can also win if everyone chooses 1, but you can also lose if you choose 1 and everyone else chooses 0. If it is a random choice between 0 and 1, it seems 0 would still be the best choice
For that matter every1 can win if all of them select 100 :p
but how can i loose if i choose 1 and i' chooses 0?
 
Everyone can also win if everyone chooses 1, but you can also lose if you choose 1 and everyone else chooses 0. If it is a random choice between 0 and 1, it seems 0 would still be the best choice
If everyone chooses 0 and you choose 1, then the max of all stated # is 1. 2/3 of 1 is 2/3 - which is closer to 1 than 0.
 
If everyone chooses 0 and you choose 1, then the max of all stated # is 1. 2/3 of 1 is 2/3 - which is closer to 1 than 0.
You have to divide that by 100 (it is the average after all) so 0 would be closer to 2/300
 
If everyone is rational (and only integers are chosen), then the only pure-strategy Nash equilibria are 0 or 1. I believe there are no mixed strategies, but it's been a while since I've done game theory so I'm not sure.

Edit: Whoops, I did average instead of max
 
But I might think that everyone will select one .... so I will select 100 to win..
 
In my opinion, if we consider this as a total stochastic process, the probability of no one choosing 100 is quite low, and 67 is definitely the best choice.
But actually, 100 is not really big enough, so maybe 67 is the best choice when there are 100000 or more people.

On the other hand, if the best choice does exist, I highly doubt that there is any better strategies than choosing 1. Suppose the best choice is X, and I'm sitting in the classroom of Harvard or MIT where everyone else is just too clever not to choose X, then the best choice in this particular case becomes X*2/3. Only if X=0 or 1 will this contradiction be resolved, and as stated above, 1 is better than 0.

Guessing only, anyone has better ideas?

I think the probability of no one choosing 100 is 1. Why would any rational player choose 100 and expect it to be (2/3)rd of the maximum chosen no., when the maximum chosen no. itself can at most (theoretically) be 100? No one would. And since no one would expect anyone to choose hundred, no one would choose 67 either. Since no one would choose 67, no one would choose (2/3)rd of 67 either. This, I think, will go on and on, and consequently, I'm tempted to say that '0' (zero) should be the answer.
 
if you compare 1 to 100 , (I haven't studied game theory ever, so correct me if I am wrong) I think 100 also strictly dominates 1.
So sushant now you have a reason why someone may choose 100 and actually win :p
Although 100 isn't an optimum number to pick if you are trying to beat 1
 
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