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The Poisoned Cup, revisited


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#1 Yoruichi-san

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Posted 08 June 2012 - 06:59 PM

Many games, in fact, probably most games, do not have an optimal solution or Nash equilibrium, that is, if a player chooses one strategy, his opponent(s) always can do better for themselves by changing to a different strategy.

One such example is the infamous "which is the poisoned cup?" scenario, in which, for example, if the poisoner picks the strategy "he thinks I'm going to put it in his cup, so I'll put it in mine", then the poisonee is incentivized to move to the strategy "he thinks I think he's going to put it in my cup, so he'll put it in his, so I'll pick mine," and the poisoner then is incentivized to change to "he thinks I think he thinks..." and so on and so forth.

However, there are strategies that, once adopted, force a local equilibrium, that is, the players involved have no incentive to change strategies.

Now let's make this slightly more interesting...let's say that one cup contains water and the other coffee, which, due to its antioxidant properties *cough* makes the poison 20% less effective, that is, it will only kill you 80% of the time. Find equilibrium strategies for this scenario.

Edited by Yoruichi-san, 08 June 2012 - 06:59 PM.

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#2 WitchOfSecrets

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Posted 09 June 2012 - 12:46 AM

I don't know microecon stuff well, but my intuition says that the equilibrium strategies for the original poisoned cup scenario are:

Spoiler for too simple?


Let's see if I can start from that assumption and see how adding coffee switches the equilibrium...
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#3 WitchOfSecrets

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Posted 09 June 2012 - 08:23 AM

Here we go.

Spoiler for Intuition and calculus?

Edited by WitchOfSecrets, 09 June 2012 - 08:24 AM.

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#4 Anza Power

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Posted 09 June 2012 - 12:09 PM

Spoiler for answer

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#5 Half Fast

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Posted 09 June 2012 - 03:33 PM

Not too good at reckoning so I'll put it in the coffee, it'll probably kill them and might not kill me depending on who gets it, providing putting it in neither is not an option.
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#6 Yoruichi-san

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Posted 10 June 2012 - 12:26 AM

Here we go.

Spoiler for Intuition and calculus?


Very good! You even did the full analysis with calculus...hmm...I'm going to have to figure out a special symbol to give out...maybe the ITG double star?

Spoiler for An alternative method for finding the solution

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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page! Episode 3 is finally here!

When life hands me lemons, I make invisible ink.




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