Guess Number play

[Sushant]

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

I think the way you choose your answer should not be based on "what you think others 'might' choose" but on "what you think others, rational that they are like you, 'must not' choose". I haven't studied game theory much, but I know that a general premise of game theory is to consider all your opponents smart (more accurately: rational). Or in other words, you should tell yourself that whatever you're thinking they'd think too (basically that you can't outsmart them, your best bet is to act rationally).

 

[darth]

I think the way you choose your answer should not be based on "what you think others 'might' choose" but on "what you think others, rational that they are like you, 'must not' choose". I haven't studied game theory ever either, but I know that a general premise of game theory is to consider all your opponents smart (more accurately: rational). Or in other words, you should tell yourself that whatever you're thinking they'd think too (basically that you can't outsmart them, your best bet is to act rationally).

So whatever I think they will think too , so all of us will always win irrespective of what i think... I dun suppose this logic holds...

 

[ferdowsi]

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

It depends on the payoffs. If the prize is split among all the winners, then 100 does strictly dominate 1. If winners get the same amount no matter how many winners, then 100 dominates 1 but not strictly (everyone choosing 1 gives you the same outcome as everyone else choosing 1 and you choosing 100). In terms of determining equilibria, strict dominance vs. dominance is an important distinction.

 

[ferdowsi]

If we consider the case where the prize is split among all winners, then there is no pure-strategy equilibria (i.e. if everyone chooses a number with 100% certainty, then at least 1 person will want to deviate). Of course, by Nash's theory, there is some mixed equilibria (though I'm not sure what that is at the moment).

 

[aaronhotchner]

It should still get pushed to 0. If the maximum number chosen is X, I want to be as close to 2X/3 as possible, and the best way to do that is to choose 0 so that I'm exactly correct. This is especially true in a repeated game; you probably won't see this in a one-shot competitive game. Over time, though, people discover the maximum number chosen and will gravitate toward 2/3 of that number, and then you're stuck in a constantly decreasing trend until everyone just picks 0, and then no one has an incentive to change. Nash equilibrium.

And yes, I have studied game theory.

 

[ferdowsi]

It should still get pushed to 0. If the maximum number chosen is X, I want to be as close to 2X/3 as possible, and the best way to do that is to choose 0 so that I'm exactly correct. This is especially true in a repeated game; you probably won't see this in a one-shot competitive game. Over time, though, people discover the maximum number chosen and will gravitate toward 2/3 of that number, and then you're stuck in a constantly decreasing trend until everyone just picks 0, and then no one has an incentive to change. Nash equilibrium.

And yes, I have studied game theory.

If there is 1 prize divided among winners, then picking 0 is definitely not Nash. In that case, everyone has an incentive to alter their strategy. If winners each always get the same amount, then yes, 0 is a Nash equilibrium. However, it's not a very stable one as a "trembling hand" error on the part of any of the other 99 players means that you lose.

 

[aaronhotchner]

I suppose the game needs to be more well-defined, then. I just want to "win." If there is an advantage to being the only winner, there likely is no equilibrium -- nobody wants to pick the highest number (unless only integers are allowed, then I guess everyone wants to pick 1 -- but there still won't be one winner), and therefore the rational move is to get closer and closer to 0 (again with the exception that we can only pick integers).

 

[ferdowsi]

I suppose the game needs to be more well-defined, then. I just want to "win." If there is an advantage to being the only winner, there likely is no equilibrium -- nobody wants to pick the highest number (unless only integers are allowed, then I guess everyone wants to pick 1 -- but there still won't be one winner), and therefore the rational move is to get closer and closer to 0 (again with the exception that we can only pick integers).

There is no pure-strategy equilibrium. However, there is a mixed-strategy equilibria. Nash received the Nobel proving that.