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        riddles >> easy >> game of Greed
        
(Message started by: JocK on Dec 3rd, 2004, 1:49pm)
Title: game of Greed
Post by JocK on Dec 3rd, 2004, 1:49pm
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!
Title: Re: game of Greed
Post by JocK on Dec 3rd, 2004, 2:24pm
Just for completeness:

the pay-out table (your net gains depending on the two possible bids you can make)
Title: Re: game of Greed
Post by Barukh on Dec 4th, 2004, 7:12am
Just a guess: is it related to Prisoner's Dilemma (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_medium;action=display;num=1033124897;start=6)?
Title: Re: game of Greed
Post by JocK on Dec 4th, 2004, 2:22pm

on 12/04/04 at 07:12:26, Barukh wrote:
Just a guess: is it related to Prisoner's Dilemma (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_medium;action=display;num=1033124897;start=6)?

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_medium;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_putnam;action=display;num=1101758336)
Title: Re: game of Greed
Post by Grimbal on Dec 4th, 2004, 3:42pm
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.
Title: Re: game of Greed
Post by Icarus on Dec 4th, 2004, 4:45pm
This was my thought too. The payoff for cooperating is too small to justify the risk.
Title: Re: game of Greed
Post by Barukh on Dec 5th, 2004, 1:06am

on 12/04/04 at 14:22:59, JocK wrote:
(B.t.w. can't see the start of the thread quoted in your post.)

It's originated at the Riddles (http://www.ocf.berkeley.edu/~wwu/riddles/medium.shtml#prisonerDilemmaRedux) page.
Title: Re: game of Greed
Post by JocK on Dec 5th, 2004, 2:36am

on 12/04/04 at 15:42:49, Grimbal wrote:
... I expected that outcome since I expected only half the players to collaborate.



on 12/04/04 at 16:45:17, Icarus wrote:
This was my thought too. The payoff for cooperating is too small to justify the risk.


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).
Title: Re: game of Greed
Post by Barukh on Dec 5th, 2004, 5:00am

on 12/05/04 at 02:36:31, JocK wrote:
Any of the zero-bidders who is willing to explain their considerations?

I was one of the zero-bidders, but don’t kill me for that…  ;D I am not an expert in game theory. So, here’s my 1 cent:


on 12/05/04 at 02:36:31, JocK wrote:
Yes, no matter what the other four do, it is never profitable to collaborate (make a zero bid).

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 (http://en.wikipedia.org/wiki/Nash_equilibrium#Prisoner.27s_dilemma) is an interesting remark on it related to this problem.
Title: Re: game of Greed
Post by JocK on Dec 5th, 2004, 7:33am

on 12/05/04 at 05:00:25, Barukh wrote:
... you would make a $1M bid? And what if everybody thinks the same way ... ?


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 12/05/04 at 05:00:25, Barukh wrote:
Besides – correct me if I am wrong – your conclusion follows from what is called Nash Equilibrium. Here (http://en.wikipedia.org/wiki/Nash_equilibrium#Prisoner.27s_dilemma) is an interesting remark on it related to this problem.


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...  :(
Title: Re: game of Greed
Post by rmsgrey on Dec 5th, 2004, 12:17pm
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]
Title: Re: game of Greed
Post by Icarus on Dec 5th, 2004, 12:23pm
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.
Title: Re: game of Greed
Post by towr on Dec 5th, 2004, 12:34pm
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.
Title: Re: game of Greed
Post by asterix on Dec 5th, 2004, 3:45pm
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.
Title: Re: game of Greed
Post by Icarus on Dec 5th, 2004, 6:23pm

on 12/05/04 at 12:34:18, 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.


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...
Title: Re: game of Greed
Post by Grimbal on Dec 6th, 2004, 4:40am
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.
Title: Re: game of Greed
Post by towr on Dec 6th, 2004, 7:26am

on 12/06/04 at 04:40:19, Grimbal wrote:
I think the error in the reasonning is to believe that by betting $0 you somehow make the others bet $0.
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.
Title: Re: game of Greed
Post by Grimbal on Dec 6th, 2004, 7:58am
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.
Title: Re: game of Greed
Post by towr on Dec 6th, 2004, 8:18am
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.
Title: Re: game of Greed
Post by Grimbal on Dec 6th, 2004, 9:31am

on 12/06/04 at 08:18:50, towr wrote:
Depends on your definition of rational. Someone has to make a sacrifice. It's not rational to expect others to do so.

But what else can you do do improve your profit?

Quote:
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.

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?
Title: Re: game of Greed
Post by Three Hands on Dec 6th, 2004, 10:51am
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 ;D
Title: Re: game of Greed
Post by rmsgrey on Dec 6th, 2004, 1:20pm
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?
Title: Re: game of Greed
Post by towr on Dec 6th, 2004, 1:39pm

on 12/06/04 at 09:31:02, 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?
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?
Title: Re: game of Greed
Post by towr on Dec 6th, 2004, 1:45pm

on 12/06/04 at 13:20:14, 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?
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.
Title: Re: game of Greed
Post by Zeke the Geke on Dec 6th, 2004, 1:50pm
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.
Title: Re: game of Greed
Post by JocK on Dec 6th, 2004, 2:05pm

on 12/06/04 at 13:50:02, 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.
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... ;) )
Title: Re: game of Greed
Post by JocK on Dec 6th, 2004, 2:15pm

on 12/06/04 at 04:40:19, Grimbal wrote:
I think the error in the reasonning is to believe that by betting $0 you somehow make the others bet $0.

Yes, difficult to see how anyone one can argue against that!


on 12/06/04 at 07:26:57, 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.

Thanks to folk who reason like this, the rational $1M bidders indeed do win... ;D

Title: Re: game of Greed
Post by towr on Dec 6th, 2004, 2:24pm
So? I wouldn't get anything otherwise anyway, good luck to them :P
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'.
Title: Re: game of Greed
Post by JocK on Dec 6th, 2004, 3:00pm

on 12/06/04 at 14:24:05, towr wrote:
So? I wouldn't get anything otherwise anyway, good luck to them :P
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'.


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... ;)
Title: Re: game of Greed
Post by Icarus on Dec 6th, 2004, 3:01pm
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.
Title: Re: game of Greed
Post by Grimbal on Dec 7th, 2004, 1:29am

on 12/06/04 at 13:39:53, towr wrote:
That's not equivalent, because it will cost you something, in this puzzle it costs you nothing.

It will cost you the chance of earning money if anybody else is so generous as to bet $0.
Title: Re: game of Greed
Post by towr on Dec 7th, 2004, 1:38am

on 12/06/04 at 15:00:34, JocK wrote:
If one of the other four happens to bid $0, you still don't win anything.
Yes I do, with 50% probability.
Title: Re: game of Greed
Post by Grimbal on Dec 7th, 2004, 1:46am

on 12/06/04 at 13:20:14, 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?


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.
Title: Re: game of Greed
Post by towr on Dec 7th, 2004, 1:53am

on 12/07/04 at 01:29:05, Grimbal wrote:
It will cost you the chance of earning money if anybody else is so generous as to bet $0.
And what's the chance of that happening?
Title: Re: game of Greed
Post by JocK on Dec 7th, 2004, 10:15am

on 12/07/04 at 01:53:57, towr wrote:
And what's the chance of that happening?


It seems that chance is 100% if a guy named Towr participates... :)
Title: Re: game of Greed
Post by towr on Dec 7th, 2004, 1:50pm
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.
Title: Re: game of Greed
Post by rmsgrey on Dec 7th, 2004, 7:16pm

on 12/07/04 at 01:46:03, 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.

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)
Title: Re: game of Greed
Post by Grimbal on Dec 8th, 2004, 4:30am

on 12/07/04 at 19:16:40, 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)


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.
Title: Re: game of Greed
Post by rmsgrey on Dec 8th, 2004, 11:00am

on 12/08/04 at 04:30:16, 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.

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.
Title: Re: game of Greed
Post by JocK on Dec 8th, 2004, 12:52pm

on 12/07/04 at 19:16:40, 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)

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...  
Title: Re: game of Greed
Post by JocK on Dec 8th, 2004, 1:15pm

on 12/08/04 at 11:00:28, rmsgrey wrote:
Which means that no-one should be super-rational?


'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...
Title: Re: game of Greed
Post by towr on Dec 8th, 2004, 1:41pm

on 12/08/04 at 12:52:41, 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.
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 ::)
Title: Re: game of Greed
Post by JocK on Dec 8th, 2004, 3:53pm

on 12/08/04 at 13:41:21, 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 ::)

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!'...  :P
Title: Re: game of Greed
Post by towr on Dec 9th, 2004, 12:34am
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]
Title: Re: game of Greed
Post by rmsgrey on Dec 9th, 2004, 8:53am
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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