[Guest]

OK, so this is technically not a puzzle, but it's an interesting game, psychological debate, and hypothetical quandary.

You and ten other people are placed in a room. One by one the host of this little game calls you out and you are given a choice: Take $1000 dollars and go home now, or decline this offer and the host will give you $50,000 but only if everyone else declines as well! Once you make your choice, the host sends you into another room to wait anxiously while the others are given the same choice.

The main questions that I think are interesting are: (of course) Which would you pick? If the numbers were different, would you conceivably change your decision? What would be the tipping point where if the grand prize were X dollars you would wait it out?

note: This was taken from a book on the psychology of numbers, but I can't remember now the author or the title. If someone knows, please enlighten me.

[Guest]

given the choices I would expect everyone to choose to decline for the grand pirize as it seems the wiser solution. Therefore I would choose to decline based on what could I lose ya know? The worst case scenario is that I would not get any money. An interesting way to flip the page though would be to make the situation that if not everyone declined then you would owe the host $1000. In that case I would take the moey and run, quickly!!

[Guest]

sheer probability... so far, reading these posts... it seems like 1:8 choose the thousand... even if it makes more logical sense to you to get the 50,000... there is a high probability that at least one of the ten are gonna go for the 1000... so... by choosing the thousand you are betting that at least one person will choose the thousand... by choosing 50,000 you are betting absolutely nobody would... so... i choose the thousand based on the probablity that someone else will too...

[Guest]

Again, as mentioned by myself and a few others, your conclusion makes perfect sense assuming not only that everyone in the group thinks rationally, but also assuming that they all believe the others will think rationally. So if everyone in the group of ten is from this forum, or MENSA, then everyone's 50k richer, otherwise I will always trust in the irrationality others.

You are absolutely right! Game Theory is based on people acting rationally. Real world applications get fuzzy. This has been a pretty good topic so far with all the opinions and different ideas.

[Guest]

I agree with Pchands. It's pretty obvious that in a group of ten at least one will take the 1000. Therefore i would take the 1000. What would change my choice would not be different dollar amounts, but a different number of people involved.

[EventHorizon]

This game is a multi-agent form of the matrix game "stag hunt." Essentially, all players can work together and get the stag, or just hunt rabbits by themselves (and causing the ones hunting the deer to fail to get it).

There are two Nash equilibria. They are when all people take the $1,000, and when all people take the $50,000. Unfortunately, the 50000 is not a stable equilibria (if we know one person will choose the 1000, then the optimal strategy for all players is to do the same).

So.....how would you respond if the payoffs were such that if you choose 50000 and someone chose 1000, that you needed to pay the 1000 (or at least the people who chose 50000 needed to split the cost of giving 1000 to all that chose it)? What if the people that chose 50000 and didn't get it needed to pay 50000 instead? What if the people that chose 50000 and didn't get it is executed?

I think that even seeing the other players face to face may change outcomes. If everyone was in their own rooms and didn't see each other, I think 1000's would be taken more often then if all were in the same room.

If you want to see more games like this, look up "list_of_games_in_game_theory" on wikipedia (some possibilities are chicken, the prisoner's dilemma, battle of the sexes, ultimatum game, volunteer's dilemma, matching pennies). At the bottom of the page are also links to strategies.

[Guest]

In that scenario with that quantity of money I would definitely try and get the 50,000 because it's a considerable amount of money, specially on contrast with 1,000. But if it was a bigger amount of money for both, I'd probably take the money and not rely on other people to obtain anything.

[EventHorizon]

The difference between this and the prisoner's dilemma is that this is not game theory, it is psychology. Your decision is based on what you predict other, potentially irrational, people will do. Even if everyone in the experiment is totally rational and seeking to maximize their gains, they don't know that's the case. So you not only have to deal with other people being irrational, but with other rational people making decisions based on other people being irrational.

If you suspect that there might be someone in the group who would choose the 1,000, or you think that someone else might think you would choose the 1,000, then you might also choose the 1,000. Seeing some of the responses to this thread, it seems more than possible that 1 in 10 people would choose the 1,000 in such a situation.

Not exactly. Game theory has a lot to do with "what you predict other, potentially irrational, people will do." Game theory is closely related to economics, psychology, and AI. In fact, most of what is now game theory was developed by economists.

You can be risk-averse, risk-neutral, or risk-seeking. You can look at worst case payoffs and maximize that over your actions (a maximin strategy). You can play equilibria. etc.

[Guest]

Game theory is closely related to economics, psychology, and AI. In fact, most of what is now game theory was developed by economists.

Except for one important problem: classical economics is not supported by scientific observation. Most economists have, until recently, assumed that consumers behave in a certain logical and rational manner. Relatively recent experiments (I can't remember by whom) have shown that most consumers' behavior bears little resemblance to classical theory. Interestingly, the group of people whose consumer habits most closely resembled the model of the "average" consumer is paranoid schizophrenics.

In spite of this, I have to say I'm well and truly baffled by this one. Why anybody of sound mind would opt for the $1,000 is completely beyond my comprehension.

[EventHorizon]

Except for one important problem: classical economics is not supported by scientific observation. Most economists have, until recently, assumed that consumers behave in a certain logical and rational manner. Relatively recent experiments (I can't remember by whom) have shown that most consumers' behavior bears little resemblance to classical theory. Interestingly, the group of people whose consumer habits most closely resembled the model of the "average" consumer is paranoid schizophrenics.

In spite of this, I have to say I'm well and truly baffled by this one. Why anybody of sound mind would opt for the $1,000 is completely beyond my comprehension.

Exactly. Economics saw discrepancies, so they added more to game theory.

[Guest]

im sure more than 1 in 10 people would be mathmatical enough to realise that it would be good to wait, because the 'pot odds' for the 50,000 look good. therefore i would counter this and decline

being smarter than the smart people

[Guest]

This would be more of a dilema if the numbers were the other way around.

eg.

no-one accepts money --- everyobe gets $1 000

some-one accepts moneu --- they get $50 000 and everyone else leavess emtpy handed

For this example, the numbers should be closer together. Say $30 000 and $50 000