Hypothetical: $100 Game

CaptainCourtesy said:

Interesting point. Actually, you are probably correct. I am realizing that even MY premise was based on human psychology. If player A chooses $100, my position was that player B would reject that because he wouldn't be getting ANYTHING. However, by getting 0$, he wouldn't be losing anything. His position would remain as it was.

So, from a mathematical position alone, I agree with you.

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Even from a psychology standpoint I believe: though I give them no incentive to say yes either. 99/1 gives better odds at beating their psychology. But I have to assume they know I'm going to do what's in my best interest (at no cost to them) as I would assume in the vice versa if we won the first toss, and I would concede to the 100/0 deal if I were player B. And even if they disagree and shoot down my proposal, I still lose nothing.

fredmertz said:

Even from a psychology standpoint I believe: though I give them no incentive to say yes either. 99/1 gives better odds at beating their psychology. But I have to assume they know I'm going to do what's in my best interest (at no cost to them) as I would assume in the vice versa if we won the first toss, and I would concede to the 100/0 deal if I were player B. And even if they disagree and shoot down my proposal, I still lose nothing.

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But many people are not going to agree with your deal, so although you would get the most possible when someone does agree to your 100/0, you would need to consider the odds of someone actually agreeing to the proposal.

For me, there is no way that I would agree to 100/0 split unless I really believed that you might need the money more than me. Without actually knowing the person personally, anything but a 50/50 split would be rewarding greed and unfairness, and I would disagree to it on principle. I think the more uneven the money ratio is, the more likely you are to not get anything. So if you consider statistics in this, you would be most likely to make the most money (especially if you played this game often enough from either side) by always offering, and only accepting a 50/50 split (if you had little idea of when the game would actually end).

Looking at this, if I were player A I'd assume a 50/50 split would be accepted 100%. So that makes a fifty dollar gain my baseline. Anything I propose greater in my favor, I jeopardize the guaranteed 50 bucks. So the question would be how much do increase the risk of losing everything vs the potential gains. Let's say if I just tweaked the split to 51/49. I'd say you'd still get at least 90% chance of it being accepted. But is the 10% chance of losing a guaranteed 50 bucks worth the potential gain of a dollar? Math says now 50 x 100 = 500 vs 51 x 90 = 459. And I expect that trend would continue. For each increase in potential gain, you'd disproportionally increase the risk for a total loss. So a 50/50 split is likely to best choice for maximizing my gains.

Now, I believe the formula changes as we increase the total sum in question. Its easy for us as player B to reject 50 bucks or less based on a sense of fairness or personal pride. It's a small amount of money that has no impact on our overall financial status. Change the overall amount from $100 to $10,000 and now it becomes a different game. 60/40 split against Player B still gives him 4 grand. Its a lot harder to turn your back on 4K just because the other guy is getting more. And I believe the more you increase the amount, the greater disparities in the split Player B would be likely to accept. If the overall sum was a 100 million, and I as player B was offered only one million, I'd still take it. As I believe most people would.

CaptainCourtesy said:

You are assigning value to the numbers. I am not. Arithmetically, 99>1, and anything>0. The numbers are neither have value OR are valueless.

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But you are implying that a larger number of something is better, which is incorporating psychology again.

There can be value in something without human psychology being a factor. It can be caused by human biology, for example.

99 items of food > than 1 item of food > 0 items of food. Psychology does not have any bearing on that. Psychology would only come into play if the food was liked or not, thus altering the biological value by incorporating the psychological devaluation.

99 bullets in the chest < 1 bullet in the chest < 0 bullets in the chest. Again, Psychology isn't a factor. Psychology would only be a factor if one was suicidal and wanted to reject biological imperatives.

These examples do not incorporate human psychology, but it also shows that value can be assessed without psychology being involved.

One other wrinkle that might be worth considering - the setting in which the decision takes place.

I participated in studies like this all the time in undergrad in order to make some money, and the first time I ever had this scenario, my counterpart (who I never met) and I were seated at computers in different rooms. I suspect it was easier to play hardball (and to screw over the other party) when you weren't face to face.

Zyphlin said:

I think the point he's making Panache that, in regards to the game and the information provided, you are essentially in a vacuum

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Right. Which is rather my point. The false assumption here is not that people will act rationally, but rather that people exist in a vacuum. If we assume that, then there is no reason for player B to accept anything. Even if you give him the full $100, what is he going to do with it in a vacuum? You can't breath it. ;-)

99/1 if both A and B's goal is to make as much money for themselves in that one game. I'd split it 50/50 in real life.

RightinNYC said:

One other wrinkle that might be worth considering - the setting in which the decision takes place.

I participated in studies like this all the time in undergrad in order to make some money, and the first time I ever had this scenario, my counterpart (who I never met) and I were seated at computers in different rooms. I suspect it was easier to play hardball (and to screw over the other party) when you weren't face to face.

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so, was it like a repeated thing? I mean, did you do it over and over with the same person?

Because if the person I was doing it with kept trying to dick me over, I'd start doing the same and get rid of my "50/50" ideal. LOL

CaptainCourtesy said:

I already figured out this was a "trap" thread on the concept of fairness. It was pretty well played as I didn't figure it out until today, and I'm usually pretty quick at figuring out "trap" threads. It's a good exercise in examining the difference between theory and real world application.

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This scenario is actually fairly common in Game Theory. When I was in b-school just a couple years ago, my economics textbook and professor said flat-out that the "correct" answer was $99/$1. Today, I don't think you'd find many economists who would be so rash. The degree to which human psychology comes into play varies depending on the economists you're talking to, with the traditional economists favoring something approximating $99/$1, and the behavioral economists favoring something closer to $50/$50.

But in any case, it isn't a trap. This scenario doesn't render any below-the-belt punches or strawmen attacks on any particular economic philosophy. I think that it does highlight why the idea of a perfectly efficient market isn't realistic...and naturally, exposes flaws in the economic ideologies that derive from that. Yes, the idea that markets aren't efficient turns a few of the more extreme libertarian philosophies (like anarcho-capitalism) on their heads...but it also means that the three mainstream philosophies of the late 20th century (monetarism, Keynesianism, and supply-side economics) need to be rethought as well, since they are all based in part on the incorrect premise that markets are efficient.

rivrrat said:

so, was it like a repeated thing? I mean, did you do it over and over with the same person?

Because if the person I was doing it with kept trying to dick me over, I'd start doing the same and get rid of my "50/50" ideal. LOL

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IIRC, and this was a while back, it was only $10 instead of $100, we alternated back and forth between who played A and B, and they told us that the exercise would happen some number of times between 2 and 7(?). The effect was that you had a reason to play nice at the beginning, but you also could try to leverage things toward the end (though you didn't know when the end would be).

RightinNYC said:

One other wrinkle that might be worth considering - the setting in which the decision takes place.

I participated in studies like this all the time in undergrad in order to make some money, and the first time I ever had this scenario, my counterpart (who I never met) and I were seated at computers in different rooms. I suspect it was easier to play hardball (and to screw over the other party) when you weren't face to face.

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I agree that the setting definitely matters. As well as just the psychology of making someone angry face-to-face, if you actually get to see the other person you can make some assessments/stereotypes about them to gauge how they might react. For example, I think men are more likely to care about maximizing their profit, and women are more likely to care about fairness...so if I was Player A, I'd probably be more inclined to keep a greater percentage for myself if I saw that Player B was male. That may or may not be an accurate assessment...but it's probably how I would react.

Tucker Case said:

99 items of food > than 1 item of food > 0 items of food. Psychology does not have any bearing on that. Psychology would only come into play if the food was liked or not, thus altering the biological value by incorporating the psychological devaluation.

99 bullets in the chest < 1 bullet in the chest < 0 bullets in the chest. Again, Psychology isn't a factor. Psychology would only be a factor if one was suicidal and wanted to reject biological imperatives.

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Admit it - you were playing Oregon Trail while you wrote this post.

roguenuke said:

But many people are not going to agree with your deal, so although you would get the most possible when someone does agree to your 100/0, you would need to consider the odds of someone actually agreeing to the proposal.

For me, there is no way that I would agree to 100/0 split unless I really believed that you might need the money more than me. Without actually knowing the person personally, anything but a 50/50 split would be rewarding greed and unfairness, and I would disagree to it on principle. I think the more uneven the money ratio is, the more likely you are to not get anything. So if you consider statistics in this, you would be most likely to make the most money (especially if you played this game often enough from either side) by always offering, and only accepting a 50/50 split (if you had little idea of when the game would actually end).

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I don't get it, but I'd like to understand your reasoning better. So let's set it up to make sure we're clear: We are in a game. I win the first toss and get to choose how the money is split. So I choose $100 to me, $0 to you. You have two choices:

To reject it: in which case- GAME OVER - you get $0

To accept it: in which case I get $100, you get $0.00 -

Either way you get $0.00. Why would you not allow me to have $100 at no additional cost to you? It's my choice to make if you get money and you're choice if I get money. But my choice of giving you money means I get less money. Your choice of giving me money means nothing to you since you're already getting nothing. I truly don't understand your response.

Likewise, if I lost the first toss and was person B, I would expect you, Person A, to do what was best for you. If you did split it with me, I'd accept it and think you made an illogical choice. Because why wouldn't you expect me to give you the $100 at no cost to me? what would it matter to me at that point? Just because you could have done something differently? The fact is that the situation is now, do you get $100 or not. And why not? It's no cost to me.

Panache said:

You don't need to interact with them again for it to be rational, you just have to assume that neither of you exist in a vacuum. If they tell their friend, who in turn tells another friend, who observed the same phenomena from someone else who acted similarly "irrationally" then it makes the possibility of an "irrational" refusal an issue for Player A to consider. If none of the players B ever refuse the money out of spite, then it would be irrational for player A to plan for such. The only thing that makes it rational to assume that player B will behave "irrationally" is the fact that they are a member of a group that has a history of behaving "irrationally".

Given that the "irrational" behavior of the group has led to a much higher gain compared to a group that always behaved "rationally," the "irrational" behavior seems to only be irrational in the short term, but more rational in the long term.

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But the fallacy here is assuming that if YOU reject the offer when you're Player B, that other Player B's everywhere will follow suit (and that this is inherently a good thing for you). If your goal is to make as much money as possible, as opposed to making the world a better place for Player B's in the game, the rational thing to do would be to accept whatever Player A offers you, as long as it's more than $0. But the logic does change a bit if it's a repeating game rather than a one-shot.

fredmertz said:

I don't get it, but I'd like to understand your reasoning better. So let's set it up to make sure we're clear: We are in a game. I win the first toss and get to choose how the money is split. So I choose $100 to me, $0 to you. You have two choices:

To reject it: in which case- GAME OVER - you get $0

To accept it: in which case I get $100, you get $0.00 -

Either way you get $0.00. Why would you not allow me to have $100 at no additional cost to you? It's my choice to make if you get money and you're choice if I get money. But my choice of giving you money means I get less money. Your choice of giving me money means nothing to you since you're already getting nothing. I truly don't understand your response.

Likewise, if I lost the first toss and was person B, I would expect you, Person A, to do what was best for you. If you did split it with me, I'd accept it and think you made an illogical choice. Because why wouldn't you expect me to give you the $100 at no cost to me? what would it matter to me at that point? Just because you could have done something differently? The fact is that the situation is now, do you get $100 or not. And why not? It's no cost to me.

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The expectation of fair play is a part of human instinct. Watch how 5 yearolds play at some point. They will come up with some pretty elaborate rules to ensure fairness (or their take on fairness)

fredmertz said:

I don't get it, but I'd like to understand your reasoning better. So let's set it up to make sure we're clear: We are in a game. I win the first toss and get to choose how the money is split. So I choose $100 to me, $0 to you. You have two choices:

To reject it: in which case- GAME OVER - you get $0

To accept it: in which case I get $100, you get $0.00 -

Either way you get $0.00. Why would you not allow me to have $100 at no additional cost to you? It's my choice to make if you get money and you're choice if I get money. But my choice of giving you money means I get less money. Your choice of giving me money means nothing to you since you're already getting nothing. I truly don't understand your response.

Likewise, if I lost the first toss and was person B, I would expect you, Person A, to do what was best for you. If you did split it with me, I'd accept it and think you made an illogical choice. Because why wouldn't you expect me to give you the $100 at no cost to me? what would it matter to me at that point? Just because you could have done something differently? The fact is that the situation is now, do you get $100 or not. And why not? It's no cost to me.

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If we assume that each player wants to maximize their own payout and I'm Player B, then I'm completely indifferent between a $100/$0 split and a $0/$0 split. However, since I know that you COULD have potentially chosen to share the money with me but you chose not to, I'm probably more inclined to screw you over.

Kandahar said:

If we assume that each player wants to maximize their own payout and I'm Player B, then I'm completely indifferent between a $100/$0 split and a $0/$0 split. However, since I know that you COULD have potentially chosen to share the money with me but you chose not to, I'm probably more inclined to screw you over.

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I understand that's your inclination. I just don't understand why.

I think I had an epiphany and just deleted everything I just wrote. LOL. Let me start over:

So I believe that you feel that we are both entitled to the money. And so by my choosing the 100/0 option, you feel like I took something of yours because I could have made another decision and so you seek revenge on me for taking an asset to which you were entitled.

So the difference in our beliefs is this: I believe that the winner of the first coin toss has the only entitlement privelages. i.e. person A. They get to choose who gets the money and so the money is already their's IMO. They are entitled to it. I feel the coin toss was a determination of the privelage of entitlement. You feel it is just a formality and that regardless of who wins the first toss, entitlement is shared, but merely distributed by person A

fredmertz said:

I understand that's your inclination. I just don't understand why.

I think I had an epiphany and just deleted everything I just wrote. LOL. Let me start over:

So I believe that you feel that we are both entitled to the money. And so by my choosing the 100/0 option, you feel like I took something of yours because I could have made another decision and so you seek revenge on me for taking an asset to which you were entitled.

So the difference in our beliefs is this: I believe that the winner of the first coin toss has the only entitlement privelages. i.e. person A. They get to choose who gets the money and so the money is already their's IMO. They are entitled to it. I feel the coin toss was a determination of the privelage of entitlement. You feel it is just a formality and that regardless of who wins the first toss, entitlement is shared, but merely distributed by person A

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The ability to veto gives the other person some level of control over the decision making process and they feel that because they have some level of input and ownership over it, they have entitlement. Personally, I see both sides of the argument and think both are rational. But I don't believe logic or rationality will always lead to the same conclusion and there can be multiple correct takes on the same situation.

megaprogman said:

The expectation of fair play is a part of human instinct. Watch how 5 yearolds play at some point. They will come up with some pretty elaborate rules to ensure fairness (or their take on fairness)

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The expectation is fairplay, absolutely. But what in my example is unfair? I won the coin toss, I get to choose. Those are the rules. It's fair for you to decline the deal, but irrational.

fredmertz said:

The expectation is fairplay, absolutely. But what in my example is unfair? I won the coin toss, I get to choose. Those are the rules. It's fair for you to decline the deal, but irrational.

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I guess we need to go back to that other thread and discuss fairness again. :2razz:

Also, we should know by now that people are not rational beings. At least, I don't think they are.

fredmertz said:

The expectation is fairplay, absolutely. But what in my example is unfair? I won the coin toss, I get to choose. Those are the rules. It's fair for you to decline the deal, but irrational.

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It's not irrational if I'm getting $0 either way. If my financial outcome is the same either way, I may as well pick the outcome that gives me emotional satisfaction (i.e. screwing you over). Nothing irrational about that. Now if you had split the money $99/$1, I would agree that it would be irrational of me to reject your offer, assuming, of course, that my primary goal is to maximize my profit.

However, you shouldn't assume that I'll be rational in that situation, because many people won't. I think the optimal amount for Player A to split is probably somewhere between $50/$50 and $70/$30. That has nothing to do with Player A's altruism, and everything to do with Player A's desire to maximize his own profit, in light of the potential irrationality of Player B.

fredmertz said:

So the difference in our beliefs is this: I believe that the winner of the first coin toss has the only entitlement privelages. i.e. person A. They get to choose who gets the money and so the money is already their's IMO. They are entitled to it.

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Obviously it's much more desirable to be Player A than Player B, but Player A is not all-powerful since Player B has veto power. Player A can't just assume that Player B will accept any offer Player A makes...especially if the offer is $100/$0.

Like all variations on the Prisoner's Dilemma, this is a kinda fascinating game that ultimately really does not prove much outside of it's aspects in game theory. Since I am lazy, I would just pick 50/50 and walk out with some easy free money.

RightinNYC said:

Admit it - you were playing Oregon Trail while you wrote this post.

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You can't prove anything!




Why can't we just eat the dead oxen anyway?

fredmertz said:

I don't get it, but I'd like to understand your reasoning better. So let's set it up to make sure we're clear: We are in a game. I win the first toss and get to choose how the money is split. So I choose $100 to me, $0 to you. You have two choices:

To reject it: in which case- GAME OVER - you get $0

To accept it: in which case I get $100, you get $0.00 -

Either way you get $0.00. Why would you not allow me to have $100 at no additional cost to you? It's my choice to make if you get money and you're choice if I get money. But my choice of giving you money means I get less money. Your choice of giving me money means nothing to you since you're already getting nothing. I truly don't understand your response.

Likewise, if I lost the first toss and was person B, I would expect you, Person A, to do what was best for you. If you did split it with me, I'd accept it and think you made an illogical choice. Because why wouldn't you expect me to give you the $100 at no cost to me? what would it matter to me at that point? Just because you could have done something differently? The fact is that the situation is now, do you get $100 or not. And why not? It's no cost to me.

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I'm very much into fairness. I wouldn't have made money either way, if your offer is 100/0. But maybe you will learn a lesson in human behavior by not getting anything either. I know I will feel better that eventhough I don't get any money, neither do you. It really would be a matter of feeling entitled to something, and that something should be fairly close to $50.

I will go back on saying that I would always turn down something less than $50, but really it would all depend on my mood and financial status at the time of the game. If I really needed the money, then I would be more willing to accept less, but if I didn't need the money, then I'd be more willing to give it all up to try to prove a fairness point. I'm sure other people would choose differently, but I think very few would be willing to let you have all the money, especially if the game was only played once.

Since it's a game of chance, 50-50.