Ultimatum Game
The game is played exactly one time. The proposer has an amount of money, that they are asked to divide between themselves and the responder. If the offer is not accepted, neither player will receive any money.
So I've ten dollars. To keep the money, I must divide it with you. I could give you a dollar and keep nine, and we would both be better off - you get a dollar that you would otherwise not receive, I get nine dollars.
This would be my best strategy, maximising my own benefit.
But divers and varied experiments have shown that, irrationally, this will result in your rejecting my offer, and us both receiving nothing. Offers of less than $2 (20%) are rejected. Most offers are around 40-50%.
Folk prefer to receive nothing rather than an amount considered too small.
What this shows is that ubiquitously, folk do not make decisions on the basis of rationally maximising their self-interest. Some other factor intervenes. What that is, is open to further research.
Google it.
So I've ten dollars. To keep the money, I must divide it with you. I could give you a dollar and keep nine, and we would both be better off - you get a dollar that you would otherwise not receive, I get nine dollars.
This would be my best strategy, maximising my own benefit.
But divers and varied experiments have shown that, irrationally, this will result in your rejecting my offer, and us both receiving nothing. Offers of less than $2 (20%) are rejected. Most offers are around 40-50%.
Folk prefer to receive nothing rather than an amount considered too small.
What this shows is that ubiquitously, folk do not make decisions on the basis of rationally maximising their self-interest. Some other factor intervenes. What that is, is open to further research.
Google it.
Comments (75)
No, it shows that sometimes folk do not make decisions on the basis of rationally maximising their self-interest.
Some other factor CAN intervene.
You opened your post showing the above conclusion to be false.
That is all.
Depends what that really means. Does self-interest have to incorporate simply monetary gain? Keeping one's dignity can be in one's self-interest, perhaps. Viewing something as unfair and so proving that point can be in one's self-interest. But if it is financial self-interest, then I guess if those studies are correct to an statistical degree, it is true to some degree, still thus to be determined by more findings.
I think that's pretty much it. "Oh, I see what I'm worth to you. Guess what I can do..."
You need to recognize a person's attention to probability, odds. If the person offers $0 they know the odds of acceptance are zero or close to it. As the amount offered increases, so do the odds of acceptance. The person offering 50% of the money is making a pretty safe bet, and will still reward one's own self-interest. Therefore you cannot conclude that the person offering 50% is not "rationally" trying to maximize their own self-interest, while the person offering 10% is. Otherwise you'd have to say that buying lottery tickets is "rational". In other words, being rational is respecting the odds.
You got free money, yes? You didn't earn it, but in order to keep it, you have to share it.
By offering a paltry share, you show yourself to be an avaricious and ungracious beneficiary.
The persons - including myself - who reject such an offer are showing you that uncivic-minded individuals like yourself are not welcome in our community; a dollar will not buy you acceptance.
My sense of fairness is worth more that $1 or even $10. If it were $10,000, that would be a different thing. On the other hand, telling someone to go fry ice when he tries to stiff me for thousands might be worth it.
I agree. Also, for most of us, $10 is no big loss. Screwing someone who's trying to screw us is worth lots more.
A nickle for me, a penny for my wife.
You're not seeing this right. I am with the person rejecting the offer. I would reject it, too.
"Self-interest" has a price tag, as in, people wouldn't do just about anything just to get "something". Because you're using me to gain an amount much higher than mine, then, I see that as unfair and I wouldn't agree to it, even if I'm "gaining" something out of it, too. The key is, how much am I helping you compared to what I'm getting.
You've forgotten capitalism already.
That depends on whether you believe in luck.
That's right, monetary value systems are based in equity, fairness. If someone else gets nine to my one, it is in my "self-interest" to reject the entire system, putting us each at zero.
"Which Rationality?" indeed.
That raise only lasts until the next cycle of inflation. If one group has an advantage over another, it tends to capitalize on the advantage, consolidate and increase its dominance. (See remuneration package of CEO's) Whether we know this consciously or intuit it, we tend to resist inequity when given a choice.
Need would be a factor, I would think. In other words, the extent to which the money is needed And need would have to be taken into account in determining what constitutes rational "self-interest."
The experiment has been done many times, in a wide variety of societies. One experiment in Indonesia used the equivalent of two weeks wages, not an insignificant amount, and found much the same result.
So you adopt the attitude of Homo Economicus? Yes, that's what games theory says we should do. But few of us actually act in this way. Offers of less then 20% are routinely rejected, despite being a win-win.
Curiously, several replies here have latched on to an explanation, with no reference to the empirical or games-theoretical research. A poor outcome.
Science Direct has a broad summation of some relevant research at https://www.sciencedirect.com/topics/neuroscience/ultimatum-game. I found the MRI data interesting, even though all it essentially says that fairness, and punishing perceived unfairness, feels good.
Evolution of fairness in the one-shot anonymous Ultimatum Game suggests that there is a heuristic response at work here, applying a stochastic games theoretical strategy; that fairness is a response to uncertainty.
What I'm interested in is that the game shows that we intuitively reject the correct games-theoretical response, which is to accept any offer. Compare that with the recent discussions here of Moore's arguments that we intuit the good.
Is our intuition of the good the manifestation of an evolved strategy? Is what feels fair is a result of natural selection towards an appropriate stochastic games theoretical strategy?
And if it is, does that matter?
Only in matters of money. Though I acknowledge that it was a training, and not a natural inclination. But I'll note that even in adopting that attitude I was attempting to say I agree that I'd tell the other guy to eat it, just to be clear. My thought was if I have what is being offered I'm in a position that I don't have to say yes. So, in fact, I have a good bargaining position compared to the other guy. The other guy can only make an offer, I'm the one who gets to say yes or no. That means the outcome depends upon my wishes, and not theirs.
It's a trained way of thinking, I'll admit.
Quoting Banno
We're on the same page with the first sentence, then. I agree that's interesting, even with upping the ante.
I only feel comfortable saying maybe on the second sentence?
Quoting Banno
I tend to believe that the social environment is where we can find causal explanations for what we feel in regards to ethical intuition.
So, in a very broad sense of natural selection, I would say yes -- but I'd hasten to add that this is an application of the notion (because nothing has been specified) of natural selection in a new domain, namely, culturally -- perhaps even anthropologically.
Quoting Banno
Heh, well, I'd say it doesn't in an ethical sense. We are, for better or worse, condemned to be free. I think Sartre got that right.
But as soon as we care about ethics, then it clearly matters because you have to know where you are to get to where you want to be.
The game has been played with pie.
Quoting Moliere
There's the joke. Ought we do what feels right and reject the unfair offer, or ought we follow the games-theoretical approach, and accept any offer? The Evolution of fairness article appears to offer a way to resolve this, if our intuition is actually the application of a stochastic strategy. But then in applying our intuition we are ipso facto applying a rule, and acting rationally.
So ought we apply the rule?
No Exit.
Yeh, tho is hell other people really?
It's a temptation to say for me, but... naw, not really.
I always look at IQ and talent as representing horsepower of the motor, but then in terms of the output, the efficiency with which the motor works, depends on rationality. Thats because a lot of people start out with 400- horsepower motors and get a hundred horsepower output. Its way better to have a 200 horsepower motor and get it all into output. So why do smart people do things that interfere with getting the output theyre entitled to? It gets into the habits, and character and temperament, and it really gets into behaving in a rational manner. Not getting in your own way.
This settles it.
Wait a minute! The output who is entitled to? And what exactly is the 'output'? Productivity in the workplace? Monetary success? Social advancement? Winning at games?
Is 'output' a means to some end or an end in itself?
Do smart people want to put out to their maximum capacity?
Suppose I'm a 'smart person'. What's my motivation?
You are simplifying the game too much. There is a downside to being a push-over who will accept the tiniest offer -- future events would tend to perpetuate this inequity. You already accepted the theory's suggestion without your own input, thereby supporting the theory's suggestion to accept what was offered to you without question.
So this strikes me as the real question, particularly whether the rejections are artifacts related to insignificant amounts being offered and whether as actual rewards increase whether rejections decrease.
Quoting Banno
I located the abstract, but couldn't find the complete study.
It stated:
"Implementing the ultimatum game experimentally in Indonesia makes it possible to raise the stakes to three times the monthly expenditure of the average participant. Contrary to predictions in the literature, the results show no evidence of approaching the sub-game perfect, selfish outcomes. Responders seem to be just as willing to reject a given percentage offer at high stakes as at low stakes, and Proposers make slightly less selfish offers as the stakes increase. "
What three times the monthly expenditure is isn't set forth in the abstract.
This site indicates average monthly expenses in Bali to be from $720 to $2,600 (in USD). This number will be lower if rent is shared. But assuming the amount was under $3,000 total, that remains low enough not to fully eliminate the variable of small amounts. https://www.google.com/amp/s/alittleadrift.com/should-you-move-to-bali/amp/
The biggest blow to this whole conversation is found here in this study that I found:
"Our main result is that proportionally equivalent offers are less likely to be rejected with high stakes. In fact, our paper is the first to present evidence that as stakes increase, rejection rates approach zero."
Below is my cite to all the abstracts, and you'll have to scroll through to find them all. As to the one cited just above, it appears in this list, but I've also screen shot it.
https://www.semanticscholar.org/paper/Raising-the-Stakes-in-the-Ultimatum-Game%3A-Evidence-Cameron/675df095394082a09803925c4d2fcaa3cbfff309
My takeaway from my hour of research here is that as actual dollars increase, rejections decrease, but to the extent we can afford to fuck those who try to fuck us, we will, but there is a limit to how much we will spend on the joy of vindictiveness.
Sounds reasonable.
I envision Banno and I sitting at the table. Banno realizing that he is the only rational one sitting at the table offers me $9 and himself $1 to maximize his gain.
Ahh, I see. The real self-interest, or greed factor does display itself, but in the actions of the receiver rather than in the actions of the one who makes the offer. That makes sense, because the one making the offer is in the unknown and must make decision based on possibility or assumed probability, and might be punished by the other for making an ill-judgement. The one receiving has only two possibilities, take, or punish the other. And the amount taken has a value in an outside system. So punishing the other, which is only a part of the experimental system, becomes less and less relevant as the reward in the outside system, which is fundamentally more important, increases.
In other words, I don't mind punishing another for bad behaviour, if it only costs me a little. And if the amount of bribery is sufficient, and the bad behaviour is rather insignificant, anyone would gladly refrain from punishing.
It seemed intuitive to me that if someone offered me say $1,000,000, my answer would be to accept it regardless because it was a very substantial, life changing amount of free money, and I couldn't reject it on some principle that the giver was receiving $9,000,000 and that wasn't fair.
Maybe this is a similar issue, but at work, we constantly have to deal with people feeling cheated when they learn a co-worker makes more than them. The disparities in pay ofter arise just from when they were hired and where the market was at the time so that long time employees might make less than a new hire. I understand the feeling, but we can't raise salaries across the board everytime there is a market fluctuation either. It's also an interesting dynamic where someone will be happy with their rate of pay until they learn someone made more than them. It's as if their pay is satisfactory as long as they are making the most.
You'd almost think that someone would rather make less somewhere else as long as they were the highest paid where they went.
What I tell people is that there is no fairness principle that determines pay and that the salary a person is willing to accept has to be based upon their own personal needs, what they believe they will be able to obtain in the market, and whether other opportunities are overall more attractive, but they're going to drive themselves crazy worrying about how much they make compared to each other person.
Maybe all of this related to what we're talking about here. It seems like it is somehow.
:up: My thoughts too.
We're getting there. Social relations have symbolic importance and money is a form of social relation, but not the only one. Of course, we're so degraded in our understanding of ourselves, we can with straight faces talk about game theory and evolution as if they matter more than the fact that we are constituted as sets of symbolic relations and don't exist as subjects outside those relations, so when we talk about rearranging them, that process has to be looked on holistically to be understood. Fracturing it into a bunch of mathematical, economic and evolutionary hoohaha is symptomatic of a deeper problem that makes such puzzles even superficially coherent. The whole discourse is intellectually stultifying imo.
Priceless.
I was thinking about this. I assume the responder is not given a chance to negotiate with the proposer. That would probably make a big difference.
I wonder if this is where the phrase "fifty-four forty or fight" came from. [lie] Little known fact - the US dollar was only valued at 94 cents back in the 1800s. [/lie]
I think this would be the issue for me. If someone tried to screw me like this, I would be temped to refuse the offer unless it were a life-changing amount. Just think of the joy of vindictiveness!
A rational analysis of the set-up recognizes it as an exchange relation between the currencies of respect and money which are transferable on the symbolic level, so any unequal division translates into an offer of money for respect. And its rational to give respect a non-zero value (even common sense informs us that in many social situations, respect can act almost indistinguishably from money, e.g. in influencing people, gaining favour etc ).
Also, note that the exchange happens on both an interpersonal and an intrasocial level (i.e. between the two game players and in their social context). On an interpersonal level, respect is valued against money as a ratio of comparative gain (80:20thats bad!..); on the intrasocial as a relative norm (...but 5000 bucks is a lot of money!). And the interpersonal and intrasocial must be taken into consideration even if the latter recedes into relative irrelevance for lower sums. So, it makes sense as per Hanovers analysis that as the sums increase the intrasocial monetary benefit begins to outweigh the interpersonal loss of respect.
Anyhow, respect (along with dignity, honour, etc, however you want to characterise it) is as real as money (and yes, pies) but these puzzles with their gerrymandered versions of rationality seem designed to obscure that.
I'm interested in why folk see someone who is giving them money for nothing as fucking them over.
Sure, they get more than you, but you still get something for nothing.
Quoting Hanover
Yep.
This is the best conclusion.
This would at the least leave my contribution as a statistical outlier, hopefully somewhat fucking the results; and perhaps have the experimenter engage in some reconceptualising by having to rethink whether my giving the whole amount to the responder counts as "sharing".
And as responder, if the amount were more than a cup of coffee, I'd take it. Again, this would be to the detriment of the experimenter. They are the ones benefiting from a refusal. Don't let them have their data for nothing.
They're not giving you something for nothing. They're giving you money to buy their right to keep some money. They are buying a favor from you, and in this fucked up scenario, we have created a market that sells favors and pays folks not to randomly deprive money from strangers.
I'm not sure what these experiments really show other than how otherwise normal people might attempt to navigate a world where arbitrary power controls the random distribution of money. I'd suspect that after a few generations of living in such a world, behaviors would become more survival oriented. Fortunately, right now, we'd run around like chickens with their heads cut off, not knowing what makes sense because that's not how the world works.
AN interesting perspective - nice.
All the same, the responder has no monetary investment. There refusal is a net loss in economic terms. Their agreement is a win-win. This is so regardless of the money involved.
I gather we are in agreement that the experiments show that Homo Economicus is a myth, at least for small values..?
No it isn't. It is being played over and over, all the time, everywhere. If it were not so it would be of no interest to anyone. You and I may only play once, but I will get better treatment from others if it becomes known that I speak softly, but carry a big stick. this is called 'investment'. As every criminal kno.
Quoting Banno
...but less succinctly.
Because tomorrow the offer will be even worse. I'm saying the theory is wrong if it claims it is only played once. One's wages are paid weekly.
The king (the responder) tells you (the offererer) to pay him his fair tax by giving him a percentage of your crops, and if you don't, he salts your fields.
You've got to guess what fair means. If you're wrong, it's a lose/lose for both you and the king.
Homo economicus tries to be rational, not wanting to end up with nothing, but not wanting to give up most of his labor just to be allowed to keep some scraps.
The king wants to set a price. The subject wants to avoid tyranny.
I get my scenario is different. The offerer here earned his crops and the responder is an arbitrary ruler, but if you don't add a semblance of reality (as in explaining how wealth just appears in someone's hands and why they now must offer some or lose it all), I'm not sure it proves much of anything.
Quoting unenlightened
Yes.
Quoting Banno
It remains that it is dubious those rejecting an offer made an explicit decision based on an internal argument that permitting the unfairness would result in the propagation of unfair behaviour into the future, and so that it was in their best interest to reject the offer. Rather, it was based on some intuition along the lines of "this is unfair".
Such justifications are back-constructs.
Are we in agreement that the experiments show that Homo Economicus is a myth?
Yes, that's what makes it dangerous. The bigger the lie...
Again, what the ultimatum game shows is that folk do not work in this way. Our intuition is doing something more than just a straight forward self-interest.
Game theory assumes a-sociality. But you don't get me I'm part of the union. I wrote an essay on that back in the day. The prisoner's dilemma is set up to isolate, and this game is stipulated as one-shot, for the same reason: to preserve the individual free of the taint of social influence. It was always the theory of a sociopath.
Of course, isn't that obvious to you? We didn't need the experiment to demonstrate that. We have certain deep seated tendencies which some people call innate ideas. In the Plato/Forms thread we discussed the innate idea of equality. In your referenced experiment it shows up as a sense of equity. In philosophy this sense of equality serves as the basis for conceptions like "natural rights". The same intuition which makes me want to punish you for not being fair (even at my expense), also inclines me to believe in human rights and equality.
We might, as philosophers, delve into an investigation as to how such innate ideas exist,. And we'll see, as Plato did in his investigation into the meaning of "just", the reason for a wide range of human behaviours in the responses demonstrated in the experiment. There is inconsistency between individuals within one's own particular understanding of the supposed innate ideas. The supposed innate ideas manifest differently in different people. We might take this as an indication that there is no such thing as an innate idea, but if you go to the other extreme you end up in unenlighten's category of sociopath.
So we might reject the descriptive terms, "innate ideas", as wrong because they give an inaccurate impression of what is there, but we cannot deny the reality of the behaviour, and its cause, which the words are meant to refer to. The discrepancy between the description and the thing described indicates that we have a poor understanding of what is there. Therefore further philosophy is required.
You are overthinking this. We ought to do what feels right (or what you think is right - whichever word you prefer). That's just what ought means.
The experiments falsify game theory predictions. Despite all the "isn't it obvious?" sentiment going in this thread, that's not a trivial result, though not entirely unexpected. Game theory is a powerful and successful theory, whatever people say. It was never meant to represent the full extent of human relationships, but pragmatically, it works well enough in a lot of real-world situations.
Also a point about the experimental setup being artificial and unrealistic. That is common to experiments, which try to isolate certain features and exclude confounders. So that in itself is not a good criticism. In this case the idea was to draw a contrast with game theory predictions, and that means creating conditions where the kind of rational self-interest that a game theory solution would take into account would not predict the result. This is why the experiments try to rule out social factors - reputation, reciprocity and all that - which a sophisticated game-theoretical simulation could account for.
Fundamentally, humans are driven to survival, not toward selfish promotion. If it works toward our survival that we abuse one another, we will, and the same holds true for cooperation. But we don't intuit our best survival techniques a priori. We learn through trial and error (natural selection).
So, if you toss me into a dystopia where I am to decide how much to give away to avoid your spite, I'm not fully adapted to such an environment, so I may use my adaptations gained in my normal world to my disadvantage. On the planet I evolved, we have expectations that you share a certain amount with me if you expect mutual respect from me, and consequences result if you violate that norm.
This means that how your test subjects react in this generation will vary in future generations as you continue to expose people to this new adaptation.
This experiment tests adaptations, not inherent human nature. This test just reveals the incompetence of those without the agility to immediately adapt, and as @Banno even noted, some will identify they are being tested and will respond by trying to invalidate the test by offering absurd responses. This too is an evolutionary reaction, trying to eliminate a threat by those who wish to study us as objects.
We find ourselves in "dystopian" situations more commonly than you think. Evolutionary and cultural adaptations serve to improve fitness on average and over long timescales. They do not fine-tune our behavior perfectly for every possible situation that we may face in this world.
Quoting Hanover
This wording is confusing, but I think you meant that this experiment tests the ability to adapt to the situation, as opposed to acting on instinct or habit. But this too is not right: there is no right or wrong way to behave in this experiment, so those acting on instinct are not failing a test. The idea is to find out whether people will act "rationally" (in the game theoretic sense). And the conclusion is that they generally don't - presumably, because the desire for and the expectation of fairness interferes with "rational" considerations. (Could be other reasons as well, such as fucking with experimenters, but I don't think that is very common.)
Rather, you are under-thinking it. Saying that we ought do what is right is trivial; that's just what "ought" is.
The joke is that any choice is rational, hence any choice is right.
Quoting Moliere
seems to appreciate the joke. and not so much, still wanting a determination, which is somewhat of a surprise.
But you, Sophist?
It appears like you are mixing things up here. The natural tendencies which I am born with, form the basis of my intuitions, the innate features which influence my thinking. It is not I who has learned these through trial and error, these are qualities passed to me from others who lived before me. And since the qualities I get in this way, have been selected for by natural selection, rather than by the agent doing the testing, we cannot call it "trial and error". That's a different concept from natural selection. In order to call this trial and error we would need to assume an overarching "life" as a form of being, which is learning from natural selection.
So we actual do intuit our best survival techniques a priori, because they are produced prior to one's own experience, and are innate to the person. But this was not a case of learning something through trial and error, it was a case of something being produced by natural selection. On top of this, the complicating factor is that natural selection has produced the capacity for an individual to learn from one's own experiences in one's own environment, and make decisions based on these learned factors, rather than the innate features. Now the learned knowledge appears to have the capacity to overrule the innate in judgement. And, we must consider this capacity to learn anew, and overrule the selected for qualities, to be a selected for quality itself. Therefore it appears like one of the innate tendencies, which has been selected for, as well-suited for survival, is the innate tendency to allow for the innate tendencies to be overruled by something freshly learned. On the other hand, it seems like this would have to be self-destructive. Allowing all those qualities which have been selected for as best suited for survival, to be overruled by a free will whim, would have to be itself a self-destructive quality. So the basic innate tendency is a tendency toward self-destruction, nut this constitutes "survival" for that overarching being of "life".
This trivializes rationality and equivocates about normativity.
I suppose you had in mind rationalizations of subjects' choices such as this?
Quoting T Clark
Rationality implies certain shared epistemic standards. Those standards have to be at least enduring and widespread, if not permanent and universal, or they would have no meaning. Further, they cannot be inviolate, or else they would be superfluous. It follows then that not every decision is necessarily rational.
Further, "right" is not the same as "rational." Rationality is normative, but it does not represent the full extent of normativity.
Most things humans do are neither rational nor irrational, they are non-rational.
That was the intent. Here both rationality and normativity, as you can see from the replies above, provide self-serving post hoc justification.
Quoting SophistiCat
Of course.
No. I just mean that people don't normally take a rational approach to decision making. I'll go further and say that in many cases, we shouldn't expect them to. For example - this ultimatum game. It would be neither rational nor irrational for me to reject an offer. Any rational decision would have to include underlying assumptions. Those assumptions, e.g. the relative value of money and dignity, are questions of value not rationality.
This is a classic example of a simple game when done with people has far more to it that simple math would apply. The obvous place where it went wrong is here:
Quoting Banno
As already said on the first page, there's more to a game when you divide money among people. There simply ought to be a reason why you would get somehow more than others: you found or organized the event, somehow you have more claim to the money. In fact, it could be that the other person thinks it's right for you to get the nine dollars, if he or she thinks it's just.
Hence the economists would say that people maximize utility, not cash. When dividing money among people, in that utility there is also how others view you: do you seem to be fair and respectable or are you a greedy bastard.
How much is what people think of you worth?
Eight dollars?
Participants pick any number they want between 1 and 10, then the average is calculated from the answers and divided by two. Who gets closest this number wins.
Does any want to play? I will answer if at least two play this (so we get what could be called an average) or the time when I read this again.
So @Banno, @Agent Smith and others, try your luck and give a number!
Assuming that 1 and 10 are included, and that fractions are rounded, and given that it's past my bed time, I think 1 is the Nash equilibrium.
Assume a large number of players, choosing randomly. Then the average will be 6. Half six is 3, so one should say 3. But folk will think of this, and say 3; so I should say 2 (1.5 rounded); but then everyone will say the same, so I shoudl say 1.
As will you. Everyone wins.
I lied, I didn't choose. :blush:
This is the problem with telling people it is "a game". Then the psychology of game play, competition and all sorts of things, enters the picture. And we'll try all kinds of tricks, strategies, to get as much advantage as possible, on the other, without crossing the line of cheating, upon which one would be expelled from the game.
This is the problem with the op, as expressed. It doesn't make clear whether the "players" are told whether they are playing a game or not. If they are simply told the rules, and proceed, that means one thing. If they are told that they are playing a game, that sets completely different stakes. And even just giving the players a set of rules implies that they are playing a game, so that it's a game, and there's different stakes, is unavoidable. And because "the game" is an entity itself, distinct from the person's real life existence and association with money, the person's way of dealing with money will differ. This is probably how gamblers come to feel comfortable with high stakes games, they disassociate the money in the game from their real life relation to money.
So if you pull out the Monopoly board and say we're going to play this game of Monopoly, and the starting amount is 70/30 in your favour, I'd say fuck you, put your game away, I'm not playing. That the game of the op uses real money is just a ruse thrown in by the creators of the game, intended to create ambiguity as to the objective of the game. The stakes are unrevealed. So you urge me on, and say come on play Monopoly with me, it's real money we're playing with, so you really can't lose. I'd be even more inclined to say fuck you, you deceptive bastard, quit messing with my head, I'm losing just by agreeing to play.
Metaphysicians would know ... :up:
Yep, that is what game theory says.
I pick number 10.
As @Agent Smith didn't choose a number, it's a bit one sided as there are so few players.
If we would have had the option of starting from 0, then the "Nash Equilibrium" would have been 0 and indeed everybody choosing 0 would have won, assuming that all people pick that. Still I would have chosen 10. Why? Well, my preferences isn't to play along the Nash Equilibrium line, but to give the person (if there is one) not taking the "Nash Equilibrium", but a higher number to win. Yes, I'll surely loose, but for me all those picking up the Nash Equilibrium losing gives far more pleasure / utility. Hence if @Agent Smith would have chosen 2, he would have won because average from 13 is 4,333... and divided by two is 2,1666... thus the correct wouldn't have been 1.
And this underlines the fact that when dealing with people, just like when dividing money among a group of people, the utility function and the utility which people have differs from simply maximizing behaviour that simple game theory assumes them to have. Maximizing profit is so easy to mathematically to calculate, but it's utility, not only profit, in the real world.
In physics the math works, but in economics the models are far too simple to take into account reality. The error is to think that the crude simple models of economics really portray reality and you can use math like in physics.
Muchas gracias for making me a winner in some hypothetical universe. :smile: