Keep/Share Problem

[Tom O'Donnell]

I got this yesterday in my email. I have already responded with my choices and will post them later. If you were in my situation, what would you choose in each of the three scenarios and why?


"Dear survey participant,

You recently participated in a research survey at www.chessbase.com . A total of 1049 players participated in the survey and the lottery. In the $500 lottery, you have been drawn as one of 80 who continue to the final step. Among these 80 players, two finalist will be drawn. The two finalists can choose between sharing or keeping. If both choose sharing, you each get $300, if both choose keeping you get $200 each. If you choose keeping and the opponent sharing, you get the $500 and the opponent nothing and vice versa. You will be matched against either another chess player, a primitive computer or an intelligent computer. The primitive computer randomizes between sharing and keeping (with equal probability). The intelligent computer chooses rationally. You stated your choice in the previous survey but are now asked to reconsider and you may choose differently depending on whether you are matched against:



1. 1. Another chess player

2. 2. A primitive (randomizing) computer

3. 3. An intelligent (rational) computer



If you want to complement your previous decision, please reply to this email by simply stating



1. 1. Share or Keep

2. 2. Share or Keep

3. 3. Share or Keep



If you choose not to answer this email your initial choice remains. However, if you reply to this email and are drawn as a winner you will receive an additional $100.

Thank you for contributing to research

Best regards,

Patrik Gränsmark

The Swedish Institute for Social Research"

[Zeljko Kitich]

Re: Keep/Share Problem

I got this yesterday in my email. I have already responded with my choices and will post them later. If you were in my situation, what would you choose in each of the three scenarios and why?


"Dear survey participant,

You recently participated in a research survey at www.chessbase.com . A total of 1049 players participated in the survey and the lottery. In the $500 lottery, you have been drawn as one of 80 who continue to the final step. Among these 80 players, two finalist will be drawn. The two finalists can choose between sharing or keeping. If both choose sharing, you each get $300, if both choose keeping you get $200 each. If you choose keeping and the opponent sharing, you get the $500 and the opponent nothing and vice versa. You will be matched against either another chess player, a primitive computer or an intelligent computer. The primitive computer randomizes between sharing and keeping (with equal probability). The intelligent computer chooses rationally. You stated your choice in the previous survey but are now asked to reconsider and you may choose differently depending on whether you are matched against:



1. 1. Another chess player

2. 2. A primitive (randomizing) computer

3. 3. An intelligent (rational) computer



If you want to complement your previous decision, please reply to this email by simply stating



1. 1. Share or Keep

2. 2. Share or Keep

3. 3. Share or Keep



If you choose not to answer this email your initial choice remains. However, if you reply to this email and are drawn as a winner you will receive an additional $100.

Thank you for contributing to research

Best regards,

Patrik Gränsmark

The Swedish Institute for Social Research"

This sounds a lot like the classic prisoners dilema. In that case sharing is the best option. http://plato.stanford.edu/entries/prisoner-dilemma/

[Jonathan Berry]

Re: Keep/Share Problem

Sharing is the best option, but the people running such tests have an axe to grind, which is that a "rational" competitor will choose Keep. So I'd choose Share, but Keep with the so-called rational computer, since there is, potentially, money on the line.

Of course, you don't need to believe me, you could try to investigate the biases of those running the tests. But you might not choose to make that sort of effort unless there is "real" (I mean a lot of) money on the line.

In these sorts of puzzles, it makes a difference whether you conceptualize that the test will be repeated, and the $ value of the prize makes a difference too. In the classic study, if the pot is $10, and you're offered $1, well, of course you reject because the competitor is an a-hole. But if the pot is $1,000,000 and you're offered $100,000, you probably accept because $ are $. But no researcher is going to offer a million-dollar pot.

Some people, when offered 5-5 (which anybody would accept with gratitude, eh?), decline because in their culture the host should offer more than half to the guest. It throws talk of rationality out the window. </rant>

Another factor is "where does the money end up"? The so-called computer competitor is in fact the researcher. It might make a difference to your choice if the money won by a non-person went to a food bank, or a chess federation, or a banker, or ....

[Aman Hambleton]

Re: Keep/Share Problem

This sounds a lot like the classic prisoners dilema. In that case sharing is the best option. http://plato.stanford.edu/entries/prisoner-dilemma/

A well known and highly intriguing problem.

From a human perspective though, if you choose sharing in the initial situation, you are either getting 300$ (they share too) or 0$ (they keep). If you choose keeping, then you are either getting 500$ (they share) or 200$ (they keep). The fear of getting 0$ is what gets so many people picking "keep."

Another related problem is the Monty Hall problem: http://en.wikipedia.org/wiki/Monty_Hall_problem In this problem, its more beneficial to "switch" your answer when asked again, even though it may be counter-intuitive to do so since it appears to not matter.

And interestingly enough, there also used to be a TV show about EXACTLY this. It was highly entertaining to watch - the show is called Golden Balls:

http://www.youtube.com/watch?v=p3Uos2fzIJ0

[David Ottosen]

Re: Keep/Share Problem

You might enjoy the show "golden balls" from the UK - it's a game show where it comes down to two contestants and they have this option for whatever kitty they've generated. The only choice is always to keep, no matter who your opponent is.

[John Upper]

Re: Keep/Share Problem

the Share option ("don't confess" in prisoner's dilemma) is optimal only in iterated PD, not for one shot games.

[Normand Arsenault]

Re: Keep/Share Problem

the Share option ("don't confess" in prisoner's dilemma) is optimal only in iterated PD, not for one shot games.

Your rating has reached an all-time high of 2293. What do you account this to?

[Vlad Dobrich]

Re: Keep/Share Problem

This is not a difficult decision.

If you choose KEEP >>>>>

your opponent has two options...
if he also says keep, you win $200
if he says share, you win $500
If its 50/50 what he chooses, you win on average (500 + 200)/2 = $350
In any event , you are guaranteed $200.
If you opt for SHARE , you have a 50-50 chance at $300 but also at ZERO,
so you average $150 against random plays.
So you must go for the $350 average return.
For this to be a coin flip decision, the share/share payoff must be $700 - thus
half the time you win $700 and the other half zero to average $350.
HOWEVER, each player must consider the marginal utility of the extra $350 he
can win. Thus if a player has no money the $350 has considerable value while
an additional $350 has somewhat lesser value than the first $350.
To a wealthy person, each additional $350 has approximately equal but
incrementally lesser value.

[Tom O'Donnell]

Re: Keep/Share Problem

I chose keep for all three scenarios.

I agree that the scenario with the random computer is pretty obvious for the reasons that Vlad Dobrich outlined. And to me there didn't seem to be any difference between whether I was up against a fellow chessplayer or an intelligent computer; in either case keeping seemed the better option.

To Dave O: I did take a look at some episodes of Golden Balls earlier today on YouTube. I wondered if you could whip out say 10Gs cash, give it to the show's host for safekeeping and tell your opponent that you were definitely picking steal for say the 50K so if they wanted anything they better pick share and at least they would have 10K for their troubles. Sort of like playing chicken with a couple of cars and ripping out the steering wheel in front of the other driver well before collision time.

BTW, there are maybe five people in the world whose word would have enough weight with me that I would go along with their proposal not to choose steal (i.e. if they told me they would choose share I would believe them enough to gamble on splitting the money).

[Vlad Dobrich]

Re: Keep/Share Problem

Another conundrum which perhaps cannot be solved as it seems to be a paradox.>>>>>

You are a contestant on a TV show and win a cash prize which is concealed in one of two envelopes. You may choose one of two envelopes to see how much you have won. You are told that one envelope has twice as much as the other in the form of a cheque so you can not tell by the thickness how much is in it.
You choose one of the envelopes at random, open it and see that you have won $400. So now you know the other one has either $200 or $800 in it. You now have the option to take the sealed envelope instead. Should you?
Do you give up the $400 and take the other which has a 50/50 chance at $800 but at least has $200? If you were given this option many times you would average ($800 + $200)/2 or $500 thus the odds are in your favour to gamble on the second envelope.
The problem arises that whatever amount you find in the first envelope, it seems always beneficial to choose the second. So, you don't bother opening the first envelope and take the second immediately. The paradox is that once you take the second envelope and open it, the same calculation of equity forces you to choose the first as a replacement.
So, it seems, each time you change your selection you increase the equity value and so flipping back and forth enough times should make you a millionaire!!:)

[Jonathan Berry]

Re: Keep/Share Problem

Inspired by Vlad's engineering model of a snow vehicle with wheels consisting of three circular segments ... here's my solution to the paradox.

Imagine that there are three cheques $2, $4, and $8. You draw one to put in an envelope. If you drew $2 or $8, you must put $4 in the other envelope. If you drew $4, then you may draw again. Now you draw envelopes; there's a 50% chance that you've drawn the $4 envelope, then 25% each for $2 or $8. If you drew the $4, then your chances of drawing $2 or $8 for the second envelope are equal, and you will end up with $5 average, just as Vlad put forward. But if you first drew $2 (25%), then the second envelope will be $4 (gain $2). If you first drew $8 (25%), then the second envelope again will be $4 (lose $4). So 50% of the time you gain on average $1, 25% of the time you gain $2, and 25% of the time you lose $4. 2*1 + 2 = 4. So it all comes out even and there is no paradox.

It took waaaay too long to figure that out, and I still barely believe it, so it's a good thing for me that I'm no gambler. I'd be an easy mark.

I will also allow that the puzzle at hand is different from the classic puzzle where one side decides how to divide the pot, and the other decides whether to accept the division or forfeit the pot for both sides.

There are American TV shows which involve fistfights among the participants. I wonder if you ran this puzzle on one of those shows, whether you'd get different results ....

[John Upper]

Re: Keep/Share Problem

Your rating has reached an all-time high of 2293. What do you account this to?

either studying chess 5+ hours a day, or some sort of ratings miscalculation by the CFC. ;)