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Topic: game of Greed (Read 1744 times) |
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JocK
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Re: game of Greed
« Reply #25 on: Dec 6th, 2004, 2:05pm » |
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on Dec 6th, 2004, 1:50pm, Zeke the Geke wrote:Would be nice to know if the $1 mln must be paid before or after receiving the prize. If it must be paid before the prize, that raises the likelihood of someone bidding $0. Just a thought.
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I don't see why it should raise the likelihood of someone bidding $0.
But in any case: you don't pay in advance: your payout gets compensated by your bid amount and you receive your net gain afterwards.
Would you have to pay in advance, this would cause all kind of unwanted side-effects to the game (such as poor and egocentric fellows like me preventing from take part...  )
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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JocK
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Re: game of Greed
« Reply #26 on: Dec 6th, 2004, 2:15pm » |
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on Dec 6th, 2004, 4:40am, Grimbal wrote:| I think the error in the reasonning is to believe that by betting $0 you somehow make the others bet $0. |
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Yes, difficult to see how anyone one can argue against that!
on Dec 6th, 2004, 7:26am, towr wrote:
You have to brake the stalemate somehow. Because if no one does you all lose, so you might just as well. So flip a coin or role a dice or something.
If no one risks 'loosing', no one risks winning. |
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Thanks to folk who reason like this, the rational $1M bidders indeed do win... 
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| « Last Edit: Dec 6th, 2004, 2:17pm by JocK » |
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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towr
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Re: game of Greed
« Reply #27 on: Dec 6th, 2004, 2:24pm » |
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So? I wouldn't get anything otherwise anyway, good luck to them 
Besides it's a 50-50 (or some other) chance, if any of the others follows the same method as I, I still have a chance to win something rather than nothing if all were 'rational'.
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JocK
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Re: game of Greed
« Reply #28 on: Dec 6th, 2004, 3:00pm » |
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on Dec 6th, 2004, 2:24pm, towr wrote:So? I wouldn't get anything otherwise anyway, good luck to them
Besides it's a 50-50 (or some other) chance, if any of the others follows the same method as I, I still have a chance to win something rather than nothing if all were 'rational'. |
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If one of the other four happens to bid $0, you still don't win anything. Unless... you join the rational players and change your defeatist $0 bid into a $1M bid...
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| « Last Edit: Dec 6th, 2004, 3:02pm by JocK » |
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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Icarus
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Re: game of Greed
« Reply #29 on: Dec 6th, 2004, 3:01pm » |
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In my own reasoning, I assumed my only motive was to increase my expected gain. Altruism or other factors did not come into play. In a real situation, I possibly would follow towr and asterix in betting $0, because there are other things I value more than money. So my decision would depend on the circumstances.
From the perspective of only maximizing my gain, the flaw in asterix and towr's argument is this: they assume that all players are like themselves. If they choose to defect, then so will everyone else. So there is no gain from defecting, and one might as well cooperate for the probability that everyone else will to, or at least the booby prize of feeling good about yourself. But there is no assumption in this puzzle that all players are rational, or in any way may be expected to come to the same conclusion. As a general rule, real people don't, as the poll has demonstrated.
This diversity seriously decreases the chance for cooperating to be effective, but offers a significant chance that defecting will.
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Grimbal
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Re: game of Greed
« Reply #30 on: Dec 7th, 2004, 1:29am » |
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on Dec 6th, 2004, 1:39pm, towr wrote:
That's not equivalent, because it will cost you something, in this puzzle it costs you nothing. |
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It will cost you the chance of earning money if anybody else is so generous as to bet $0.
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towr
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Re: game of Greed
« Reply #31 on: Dec 7th, 2004, 1:38am » |
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on Dec 6th, 2004, 3:00pm, JocK wrote:| If one of the other four happens to bid $0, you still don't win anything. |
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Yes I do, with 50% probability.
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Grimbal
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Re: game of Greed
« Reply #32 on: Dec 7th, 2004, 1:46am » |
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on Dec 6th, 2004, 1:20pm, rmsgrey wrote:| So what's wrong with the logic that if everyone is equally rational and has the same information available to them, then they will all follow the same strategy? |
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What is wrong is to believe that by choosing to bet $0 you make the others do the same. It is against your interest to bet $0 but it is in your interest that others bet $0. If you sum it up, it is in the interest of everybody that everybody bets $0, but you can not decide for the others, you only decide your own bet. And for yourself it is still better to be the only one to bet $1M.
If everybody is rational and egoist everybody should reach the same conclusion (in this case, bet $1M). But you can not leverage on that result and reason that if you bet $0, everybody else will.
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towr
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Re: game of Greed
« Reply #33 on: Dec 7th, 2004, 1:53am » |
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on Dec 7th, 2004, 1:29am, Grimbal wrote:
It will cost you the chance of earning money if anybody else is so generous as to bet $0. |
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And what's the chance of that happening?
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JocK
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Re: game of Greed
« Reply #34 on: Dec 7th, 2004, 10:15am » |
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on Dec 7th, 2004, 1:53am, towr wrote:
And what's the chance of that happening?
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It seems that chance is 100% if a guy named Towr participates... 
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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towr
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Re: game of Greed
« Reply #35 on: Dec 7th, 2004, 1:50pm » |
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So if I play, somebody else will always play 0? How does that make sense? (I'm not anybody else than myself)
And again, a 50% chance of me going choosing 0 isn't equal to a 100% chance.
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rmsgrey
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Re: game of Greed
« Reply #36 on: Dec 7th, 2004, 7:16pm » |
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on Dec 7th, 2004, 1:46am, Grimbal wrote:| What is wrong is to believe that by choosing to bet $0 you make the others do the same. It is against your interest to bet $0 but it is in your interest that others bet $0. If you sum it up, it is in the interest of everybody that everybody bets $0, but you can not decide for the others, you only decide your own bet. And for yourself it is still better to be the only one to bet $1M. |
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I'm not saying that my choice in any way influences everyone else's choices. What I'm saying is: if I come to a decision rationally, based solely on publically available information, everyone else will come to the same decision based on the same information. So, my rational decision is to bid X. If X is truly the optimal decision, and everyone else is as good at reasoning as me, then they will, independently, choose to bid the same value, X. If everyone is rational, and is known to be (known to be [...]) rational, then everyone will know that, whatever value they decide as a result of their rational deliberations, everyone else, starting with the same assumptions and the same reasoning power, must also come to the same conclusion. So if everyone knows that everyone is going to bid the same way, then everyone knows that if they are convinced by their own logic to bid 0, then so will everyone else be.
The reasoning can be boiled down to: Everyone is rational. If everyone is rational, they will all make the rational decision. If the rational decision were to defect, everyone would end up with nothing. If the rational decision were to cooperate, everyone would end up with $1M. The rational decision iswhatever maximises indvidual gain, so the rational decision is to cooperate.
The catch is not that you can't influence others behaviour, but that the assumption that everyone is equally rational is completely bogus. What you actually need is an estimate of the number of saints (those who will always act generously), number of sharks (those who will always defect), number of self-rationals (those who neglect the reasoning of others in favour of their possible conclusions), and number of superrationals (those who assume other superrationals will make the same decision as them). If you believe you are the only superrational present, then you should act in the same way as a self-rational. Otherwise, you should pick the strategy that maximises the gain of all superrationals - if you expect one other superrational and three sharks/self-rationals then you should adopt Towr's coin-flip - giving the sharks an expected $7M/24 and yourself and the other superrational an expected $1M/16 each (and the production company an expected 1M payout)
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Grimbal
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Re: game of Greed
« Reply #37 on: Dec 8th, 2004, 4:30am » |
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on Dec 7th, 2004, 7:16pm, rmsgrey wrote:
The catch is not that you can't influence others behaviour, but that the assumption that everyone is equally rational is completely bogus. What you actually need is an estimate of the number of saints (those who will always act generously), number of sharks (those who will always defect), number of self-rationals (those who neglect the reasoning of others in favour of their possible conclusions), and number of superrationals (those who assume other superrationals will make the same decision as them). If you believe you are the only superrational present, then you should act in the same way as a self-rational. Otherwise, you should pick the strategy that maximises the gain of all superrationals - if you expect one other superrational and three sharks/self-rationals then you should adopt Towr's coin-flip - giving the sharks an expected $7M/24 and yourself and the other superrational an expected $1M/16 each (and the production company an expected 1M payout) |
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This doesn't mean you should be superrational. If you get more than $0, it is not because you decided to be superrational, but only because others assumed that you are.
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rmsgrey
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Re: game of Greed
« Reply #38 on: Dec 8th, 2004, 11:00am » |
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on Dec 8th, 2004, 4:30am, Grimbal wrote:| This doesn't mean you should be superrational. If you get more than $0, it is not because you decided to be superrational, but only because others assumed that you are. |
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Which means that no-one should be super-rational?
In which case, the outcome of everyone behaving rationally is that no-one gets anything, while if it is more rational to be super-rational than self-rational, the outcome of everyone behaving rationally is for everyone to get $1M.
I still don't see why being super-rational is less rational than being self-rational - I can see why assuming that your reasoning is in no way unique would be unappealing, but that doesn't make it invalid.
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JocK
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Re: game of Greed
« Reply #39 on: Dec 8th, 2004, 12:52pm » |
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on Dec 7th, 2004, 7:16pm, rmsgrey wrote:
... What you actually need is an estimate of the number of saints (those who will always act generously), number of sharks (those who will always defect), number of self-rationals (those who neglect the reasoning of others in favour of their possible conclusions), and number of superrationals (those who assume other superrationals will make the same decision as them). If you believe you are the only superrational present, then you should act in the same way as a self-rational. Otherwise, you should pick the strategy that maximises the gain of all superrationals - if you expect one other superrational and three sharks/self-rationals then you should adopt Towr's coin-flip - giving the sharks an expected $7M/24 and yourself and the other superrational an expected $1M/16 each (and the production company an expected 1M payout) |
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OK, let's assume you play the game. You have made your choice: either a zero bid or a $1M bid. Subsequently all 5 bids are revealed to all 5 participants. Now, the host of the show makes you (and only you!) a special offer: you can in hindsight change your bid! Wow....! What do you do..?
Well... the answer is easy... if you have behaved like a 'shark' (made a $1M bid) you will never ever change your bid. If you are a zero-bidder however, you will at best be neutral towards your zero bid (in case all others have made a $1M bid), but in all other cases you will definitely want to change your bid.
That means that in absence of such a generous host, playing the normal game without the chance of applying hindsight corrections to your bid, you do have a down-to-earth rational bid available. A bid that you will never regret in hindsight. And that bid is, whether you like it or not, $1M...
And yes, you might in hindsight regret that others did make a $1M bid. But in this game you can't influence others...
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| « Last Edit: Dec 8th, 2004, 1:03pm by JocK » |
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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JocK
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Re: game of Greed
« Reply #40 on: Dec 8th, 2004, 1:15pm » |
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on Dec 8th, 2004, 11:00am, rmsgrey wrote:
Which means that no-one should be super-rational? |
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'Super-rationals' might ask themselves what their strategy would be in case the high bid available is not 1 million but x million (x in between 0 and 1)... Do you go for a guarenteed gain of at least 1-x million (and potentially as large as 4+x million), or do you opt for a gain of 1 million or nothing?
You might find it insightful to start with relatively small values x (e.g. x = 0.1). Now let x grow and take the limit x [to] 1. If you chnage your mind for soem value x, please explain why...
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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towr
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Re: game of Greed
« Reply #41 on: Dec 8th, 2004, 1:41pm » |
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on Dec 8th, 2004, 12:52pm, JocK wrote:| Well... the answer is easy... if you have behaved like a 'shark' (made a $1M bid) you will never ever change your bid. If you are a zero-bidder however, you will at best be neutral towards your zero bid (in case all others have made a $1M bid), but in all other cases you will definitely want to change your bid. |
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I don't think you know us well enough to say what we would definitely want to do.
If everyone had bid 0, I would probably also bid 0, even if I had bid a million before. I'm not some sort of greedy vulcan 
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JocK
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Re: game of Greed
« Reply #42 on: Dec 8th, 2004, 3:53pm » |
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on Dec 8th, 2004, 1:41pm, towr wrote:
If everyone had bid 0, I would probably also bid 0, even if I had bid a million before. I'm not some sort of greedy vulcan |
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Indeed, people who fiercly argue against the rational game-theoretical solution for a game, are usually playing an entirely different game.
This is the game 'Greed!' not the game 'Saints!' or 'Feed-the-Sharks!'...
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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towr
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Re: game of Greed
« Reply #43 on: Dec 9th, 2004, 12:34am » |
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True enough, but, there are more goals of self interest than making money. Some better served by the occasional sacrifice of fairness.
One million will suffice for most my goals, and all the girls will love me for being such a nice guy
(Survival and procreation, what more can an organism want?)
[e]And it doesn't hurt to have 4 more millionaires as friends, one of them might make an even larger fortune out of it and see it fit to repay me for giving him that chance.[/e]
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| « Last Edit: Dec 9th, 2004, 12:42am by towr » |
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rmsgrey
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Re: game of Greed
« Reply #44 on: Dec 9th, 2004, 8:53am » |
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And with a special private offer, one of the assumptions of super-rationality is broken - you now have a priviliged position and it becomes a question of what your values are.
I must say that my choice in that situation would depend on what other people had chosen. Given the opportunity, I'd probably try asking each of the others what they'd do in my position, but without actually being put in that position, I can't be sure what I'd actually do - if there's at least one of each bid without me, I'd probably switch, but if all the other bids are $0, I'd definitely stick at $0 (encouraging generous behaviour seems to me to be a strong survival trait in the long-term). If everyone else was greedy, I'd have to think long and hard.
And, of course, if I suspected the host was liable to continue changing the rules, I'd stick with $0 and let him suffer the consequences of the studio having to pay out at least $1,000,000 when he'd guaranteed they wouldn't...
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