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JocK
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game of Greed
« on: Dec 3rd, 2004, 1:49pm » |
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You are one of the five participants in the TV show known under the name Greed!. The show is to reach it's climax: a total of 5 million dollar is to be distributed amongst you and the four other participants. This works as follows:
All five candidates can bid for their share of the 5 million. They all have to make their bid simultaneously and without having any communication. Once a bid is made the participant has committed to pay the bid amount. In return, the 5 million will be distributed amongst the five participants proportional to the amount bid by each individual. To make things easy, you have only two choices for the amount to bid:
1) a bid of $0.00
2) a bid of $1 million
If all five candidates bid $1 million, the 5 million gets split equally amongst them, so that each gets $1 million. However, they also each have to pay $1 million for their bid, so that they all leave the show empty handed.
If four candidates bid $1 million, and one bids $0, the 5 million gets split equally amongst the four 'high-bidders': they all receive $1.25 million. This amount minus the $1 milion bid leaves each of them with $0.25 million. The zero bidder goes home empty handed (doesn't receive anything from the 5 million, and also doesn't have to pay anything).
Would you be the only person bidding one million, this would result in the whole sum of $5 million going your way. This amount minus the $1 million bid leaves you with the net amount of $4 million.
Would all five participants bid $0, then the $5 million gets split equally in $1 million portions: one for each of them. This $1 million constitutes the net individual gain as no bidding payment needs to be made.
Now... the time has come. You have three seconds. In that period of three seconds you either press the button "$1 mln" or you don't. You can't see what the others are doing...
What do you do..?
3... 2... 1... STOP!
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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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Just for completeness:
the pay-out table (your net gains depending on the two possible bids you can make)
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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 #3 on: Dec 4th, 2004, 2:22pm » |
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on Dec 4th, 2004, 7:12am, Barukh wrote:
If you would reduce the number of participants to two, this game would indeed get the characteristics of the well-known 'Prisoner's Dilemma'. (B.t.w. can't see the start of the thread quoted in your post.)
The nice thing about the above game is that the number of choices per participant need not be restricted to two (as is the case in the game 'Prisoner's dilemma'). Things get more interesting (and tractable using analytical methods) when we allow for what is basically a continuum of choices:
http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_med ium;action=display;num=1102196884.
Main reason for posting above poll (using a reduced form of the game) is to check to what extent forum participant are rational and to what extent social and/or irrational?  (see discussion: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_put nam;action=display;num=1101758336)
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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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Grimbal
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Re: game of Greed
« Reply #4 on: Dec 4th, 2004, 3:42pm » |
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Whatever the other players do, I am better off betting 1M.
Yes, this is egoistic. But we are supposed to be, right?
Imagine what my wife would say if I told her "I had a chance to win up to 4 million, but I choose to limit the chances to 1 million. This way, I got nothing instead of 500K. In fact, I expected that outcome since I expected only half the players to collaborate.
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Icarus
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Re: game of Greed
« Reply #5 on: Dec 4th, 2004, 4:45pm » |
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This was my thought too. The payoff for cooperating is too small to justify the risk.
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Barukh
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Re: game of Greed
« Reply #6 on: Dec 5th, 2004, 1:06am » |
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on Dec 4th, 2004, 2:22pm, JocK wrote:| (B.t.w. can't see the start of the thread quoted in your post.) |
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It's originated at the Riddles page.
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JocK
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Re: game of Greed
« Reply #7 on: Dec 5th, 2004, 2:36am » |
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on Dec 4th, 2004, 3:42pm, Grimbal wrote:| ... I expected that outcome since I expected only half the players to collaborate. |
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on Dec 4th, 2004, 4:45pm, Icarus wrote:| This was my thought too. The payoff for cooperating is too small to justify the risk. |
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Yes, no matter what the other four do, it is never profitable to collaborate (make a zero bid). The result of the poll (1/3rd collaborating) is therefore very surprising to me. OK, maybe I expected a single outlier who either misread the question, or simply is curelessly social? But 1/3rd of the population..?
Any of the zero-bidders who is willing to explain their considerations?
As an aside: if the 1/3rd cooperating in this poll is representative, in a game like this (5mln to distribute amongst five participants) the 1mln bidders can expect to gain some 500K, whilst the zero-bidders will on average go home with 12K (in one out of 81 games the other four players are expected to cooperate).
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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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Barukh
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Re: game of Greed
« Reply #8 on: Dec 5th, 2004, 5:00am » |
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on Dec 5th, 2004, 2:36am, JocK wrote:| Any of the zero-bidders who is willing to explain their considerations? |
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I was one of the zero-bidders, but don’t kill me for that…  I am not an expert in game theory. So, here’s my 1 cent:
on Dec 5th, 2004, 2:36am, JocK wrote:| Yes, no matter what the other four do, it is never profitable to collaborate (make a zero bid). |
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So, according to this, you would make a $1M bid? And what if everybody thinks the same way (assume that every participant is as good in game theory as any other – but maybe, it’s not rational to think this way)?
Besides – correct me if I am wrong – your conclusion follows from what is called Nash Equilibrium. Here is an interesting remark on it related to this problem.
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JocK
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Re: game of Greed
« Reply #9 on: Dec 5th, 2004, 7:33am » |
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on Dec 5th, 2004, 5:00am, Barukh wrote:
... you would make a $1M bid? And what if everybody thinks the same way ... ? |
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Yes, I made a $1M bid. Even if everybody else thinks the same way and also bids $1M, I am gaining as much as when I would have made a zero bid (i.e. in both cases I have a zero gain). In all other cases (at least someone of the other four bidding zero) I gain (much) more compared to the case when I would have made a zero bid.
on Dec 5th, 2004, 5:00am, Barukh wrote:Besides – correct me if I am wrong – your conclusion follows from what is called Nash Equilibrium. Here is an interesting remark on it related to this problem.
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The conclusion follows from the fact that each player has a unique dominant strategy available (dominant in the sense that the strategy under no circumstance - i.e. regardless of what the other four players decide to do - can be beaten by any other strategy). One might refer to this as a Nash equilibrium, but the term Nash equilibrium usually refers to equilibrium solutions in games in which the players don't have a single dominant strategy.
Initially I thought the above poll would lead to a trivial result (95-100 % $1M bidders). The next question would then be: "what would you bid when the two available choices were a zero-bid and a $1.01M bid?". Under these conditions no dominant strategy exists, and the question is whether a Nash equilibrium would indeed result.
But given the fact that a significant fraction of the population seems to avoid chosing a dominant strategy, no use in posting a follow-up poll... 
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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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rmsgrey
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Re: game of Greed
« Reply #10 on: Dec 5th, 2004, 12:17pm » |
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Suppose that, instead of reasoning "Everyone else will make the same choice regardless of what I choose, so since greed never loses me money, and, if not everyone else is greedy, in fact gains, I will be greedy", you instead reason that "Everyone else has the same information as me, so, if everyone else is as rational as I am, they will follow exactly the same strategy as me. Therefore, I should pick the strategy that maximises the collective gain, since I will, on average get an equal share of that gain. Since the total prize is always reduced by anyone being greedy, I should be generous."
Regrettably, the latter reasoning seems to be based on a false assumption - that everyone else is as rational as I - in fact, most people seem to have difficulty appreciating Tit-For-Tat in an iterated prisoners dilemma...
[e]Oh, and I missed the poll entirely by not getting online whileit was up, but, I would have voted $0[/e]
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| « Last Edit: Dec 5th, 2004, 12:19pm by rmsgrey » |
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Icarus
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Re: game of Greed
« Reply #11 on: Dec 5th, 2004, 12:23pm » |
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That is exactly the point. With the chance to work out with everyone else what the best approach would be, I might be willing to cooperate (depending on how trustworthy I find my companions), but with no chance to access the others, it is extremely unlikely that cooperation would work. And without some guarantee of cooperation, it simply is not worth the risk.
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towr
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Re: game of Greed
« Reply #12 on: Dec 5th, 2004, 12:34pm » |
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What risk? It's not like you can have a net loss.
There's something to be said for simply increasing the total gain. What use is it to me to bid a million for a million? Someone might as well win something, even if it's not me.
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| « Last Edit: Dec 5th, 2004, 12:35pm by towr » |
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asterix
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I was one of the 0 votes, because I'm not the kind of person who would ever be on a gameshow called Greed. I would generally expect the other 4 players to be greedy, so I'm not going to win anything anyway. And if I can increase the common good, I say go for it even if there's no gain for me. Then I contact the other players after the show and see if I can convince them to reward me for my generosity. And if they don't, I slash their tires.
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Icarus
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Re: game of Greed
« Reply #14 on: Dec 5th, 2004, 6:23pm » |
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on Dec 5th, 2004, 12:34pm, towr wrote:What risk? It's not like you can have a net loss.
There's something to be said for simply increasing the total gain. What use is it to me to bid a million for a million? Someone might as well win something, even if it's not me. |
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Sorry, I was using "risk" in a less technical fashion. More appropriate would be to say that under the circumstances, my expected outcome is higher for defecting than for cooperating.
Unless, of course I follow asterix's lead and fake altruism while attempting to blackmail...
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"Pi goes on and on and on ...
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I wonder: Which is larger
When their digits are reversed? " - Anonymous
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Grimbal
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Re: game of Greed
« Reply #15 on: Dec 6th, 2004, 4:40am » |
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I think the error in the reasonning is to believe that by betting $0 you somehow make the others bet $0.
I think collaboration works only between people acting non-rationally (for instance they try to be "fair") or where there is a possibility of retaliation.
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towr
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Re: game of Greed
« Reply #16 on: Dec 6th, 2004, 7:26am » |
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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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I think the error lies in believing you'll actually win anything if everyone bids a million.
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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| « Last Edit: Dec 6th, 2004, 7:27am by towr » |
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Grimbal
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Re: game of Greed
« Reply #17 on: Dec 6th, 2004, 7:58am » |
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If you throw a dice and bet $0 with some probability to break the stalemate, that is what I call being fair and not rational. Doing this you make a sacrifice for the others. You accept to loose a small potential profit (someone else could throw the dice) in exchange for a large benefit for all others. You don't get any benefit from it. The profit you get when everybody bets $0 is only because the other were so nice to you to bet $0. It still doesn't make it rational (if you are greedy) to bet $0.
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towr
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Re: game of Greed
« Reply #18 on: Dec 6th, 2004, 8:18am » |
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Depends on your definition of rational. Someone has to make a sacrifice. It's not rational to expect others to do so.
Game theory isn't rational if it makes everybody lose. It's not rational to adhere to a method that won't let you win. Rationally it makes sense to be 'irrational'. It's all about ecological rationality.
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| « Last Edit: Dec 6th, 2004, 8:20am by towr » |
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Grimbal
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Re: game of Greed
« Reply #19 on: Dec 6th, 2004, 9:31am » |
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on Dec 6th, 2004, 8:18am, towr wrote:| Depends on your definition of rational. Someone has to make a sacrifice. It's not rational to expect others to do so. |
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But what else can you do do improve your profit?
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Game theory isn't rational if it makes everybody lose. It's not rational to adhere to a method that won't let you win. Rationally it makes sense to be 'irrational'. It's all about ecological rationality. |
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If everybody bets $0 and I bet $1M, who wins?
The question is equivalent to something like: are you willing to give $1 if you know that to 10 persons you don't know and you will never meet it will earn $1 each?
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Three Hands
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Re: game of Greed
« Reply #20 on: Dec 6th, 2004, 10:51am » |
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Everyone's missed the small factor that, if you bid $0, then you guarantee that the gameshow sponsers (or whoever is footing the bill) is then guaranteed to make a loss, so it's in their best interesats for everyone to bid the $1mil. Hence, opting for the $0, you have the satisfaction of, while not expecting to gain any money yourself (but, let's face it, were you really expecting to gain by saying $1mil?), forcing the evil corporate machine to give up some of their money, so that the chairman doesn't get any big fat bonus from having not had to pay up
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rmsgrey
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Re: game of Greed
« Reply #21 on: Dec 6th, 2004, 1:20pm » |
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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?
Or is it just the case that the group of 5 people who each pocket $1M as a result of following this reasoning is less rational than the group who each go away with nothing?
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towr
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Re: game of Greed
« Reply #22 on: Dec 6th, 2004, 1:39pm » |
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on Dec 6th, 2004, 9:31am, Grimbal wrote:| The question is equivalent to something like: are you willing to give $1 if you know that to 10 persons you don't know and you will never meet it will earn $1 each? |
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That's not equivalent, because it will cost you something, in this puzzle it costs you nothing.
If I can get 10 people anything with no cost to myself I won't begrudge them it just because I don't get anything tangible in return.
Besides, we just get back to the point where no one get's anything when everyone is 'rational'. You can't increase your own profit, you can't lower it either, so why not help out your fellow man?
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towr
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Re: game of Greed
« Reply #23 on: Dec 6th, 2004, 1:45pm » |
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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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Personally I like it, but people aren't all the same. Some may be more/less (ir)rational than others or simply don't care one way or another.
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Zeke the Geke
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Re: game of Greed
« Reply #24 on: Dec 6th, 2004, 1:50pm » |
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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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