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dalbuc

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: June 04, 2007, 04:16:40 PM

This is a game that Game Theorists like to play. I'm curious what the responses are from people who, hopefully, don't know the "right" answer -> partially because I disagree with the "right" answer.

Here's the game:

You and a Buddy are returning from a remote Pacific island and find that the airline has damaged the identical antiques that each had purchased. An airline manager says that he is happy to compensate them but is handicapped by being clueless about the value of these strange objects. Simply asking the travelers for the price is hopeless, he figures, for they will inflate it.

Instead he devises a more complicated scheme. He asks each of you to write down the price of the antique as any dollar integer between 2 and 100 without conferring together. If both write the same number, he will take that to be the true price, and he will pay each of them that amount. But if they write different numbers, he will assume that the lower one is the actual price and that the person writing the higher number is cheating. In that case, he will pay both of them the lower number along with a bonus and a penalty--the person who wrote the lower number will get $2 more as a reward for honesty and the one who wrote the higher number will get $2 less as a punishment. For instance, if Lucy writes 46 and Pete writes 100, Lucy will get $48 and Pete will get $44.

What is the number your write and why?

All posts are opinions in case you are too stupid to figure that out on your own without me saying it over and over.
If you think Manziel is the best QB in this draft I can safely assume you are an idiot and will treat you as such.



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#1 : June 04, 2007, 04:19:07 PM

43

No clue why.

RedAlert

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#2 : June 04, 2007, 04:26:11 PM

$100, then bi tch-slap Lucy for not doing the same..

mjs020294

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#3 : June 04, 2007, 04:25:26 PM

99...hoping the other person says 100. 


Groovatron

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#4 : June 04, 2007, 04:45:05 PM

I won't play becasue I know the answer. However, I too, like Dal, do not agree w/ backward induction analysis.



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#5 : June 04, 2007, 04:49:59 PM

99...hoping the other person says 100.


what he said^^^

gone

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#6 : June 04, 2007, 06:39:28 PM

99...hoping the other person says 100. 

werks 4 me



John Galt?

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#7 : June 04, 2007, 06:49:19 PM

Both should write 99 each hoping the other wrote 100.
In any case writing anything less than 98 gives you a 50% chance of undercutting the other person which while giving you a $2 bonus, costs you the difference between your number and your partners.


Boid Fink

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#8 : June 04, 2007, 07:06:25 PM

A Beautiful Mind is one of my all time favorite movies...The Nash Equilibrium is in session...

How about all claim 0...




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#9 : June 04, 2007, 08:31:31 PM


This is actually a version of "Prisoner's Dilemma."

http://william-king.www.drexel.edu/top/eco/game/dilemma.html

JavaBuc

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#10 : June 05, 2007, 03:30:25 AM

I'd write down whatever the thing really costs.   I'm not out to rip anybody off.

dalbuc

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#11 : June 05, 2007, 09:02:49 AM

BTW, the "right" answer according to the game theorist is "2". I think most folks here went the direction I expected, and frankly that most folks do (higher numbers).


The logic for choosing 2 is explained here:

Consider a plausible line of thought that Lucy might pursue: her first idea is that she should write the largest possible number, 100, which will earn her $100 if Pete is similarly greedy. (If the antique actually cost her much less than $100, she would now be happily thinking about the foolishness of the airline manager's scheme.)

Soon, however, it strikes her that if she wrote 99 instead, she would make a little more money, because in that case she would get $101. But surely this insight will also occur to Pete, and if both wrote 99, Lucy would get $99. If Pete wrote 99, then she could do better by writing 98, in which case she would get $100. Yet the same logic would lead Pete to choose 98 as well. In that case, she could deviate to 97 and earn $99. And so on. Continuing with this line of reasoning would take the travelers spiraling down to the smallest permissible number, namely, 2. It may seem highly implausible that Lucy would really go all the way down to 2 in this fashion. That does not matter (and is, in fact, the whole point)--this is where the logic leads us.

Game theorists commonly use this style of analysis, called backward induction. Backward induction predicts that each player will write 2 and that they will end up getting $2 each (a result that might explain why the airline manager has done so well in his corporate career). Virtually all models used by game theorists predict this outcome for TD--the two players earn $98 less than they would if they each naively chose 100 without thinking through the advantages of picking a smaller number.

Whole article on this is here: http://www.sciam.com/article.cfm?chanID=sa006&articleID=7750A576-E7F2-99DF-3824E0B1C2540D47&ref=rss

All posts are opinions in case you are too stupid to figure that out on your own without me saying it over and over.
If you think Manziel is the best QB in this draft I can safely assume you are an idiot and will treat you as such.



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#12 : June 05, 2007, 09:50:50 AM


Lucy, apparently, is a damned idiot.


replica

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#13 : June 05, 2007, 09:54:35 AM

Interesting.

mjs020294

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#14 : June 05, 2007, 10:45:48 AM


Lucy, apparently, is a damned idiot.



Is she blond?

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