Given a sum of $1000, I would easily say 50/50. As others have pointed out, people can be spiteful jerks and I’d be afraid someone would turn down an offer of less than half simply because they thought I was cheating them somehow.
Are we talking Von Neumann type game theory or more modern game theory using behavioral economics? Von Neumann says give $0.01, more modern theory says the utility someone else gets out of sticking a(metaphorical) $999.99 stick in your eye for the insult your offer represented outweighs the $0.01 they stand to lose. There have been numerous studies of this ultimatum game, and the modern equilibrium seems to be somewhere around 60/40. If the recipient gets less than about 20% you can see frequent defections(the game theory term for refusing the deal).
I don’t have my references with me right now, but if you’re looking for a fairly approachable treatment of the recent work in this area you could look to Priceless: The Myth of Fair Value (and How to Take Advantage of It) by William Poundstone. He’s got a couple chapters on the ultimatum game and modern behavioral economic analysis of the game. One of the most interesting was when people played this game with elevated levels of various hormones. Testesterone, estrogen, and Oxytocin.
Enjoy,
Steven
Of course, the one important point is that real-life is not a one-shot like traditional game theory: we are a society, and traditionally (that is, evolutionally), cooperation works best. Therefore, it’s not only Schadenfreude or about pride to deny the 1st guy who offers anything less than 50/50, it makes perfect long-term sense. By stopping those jerks and showing them that their behaviour of grabbing without consideration to others is also damaging to themselves, there is a chance of stopping and changing that behavour, which is a profit long-term both the second person and to society at large.
I, too, choose 50/50, both because it’s fair, and because it has the only realistic chance of being accepted by the second person. If the first person is a friend, how could I want to cheat them? And if it’s not a friend, but a stranger, I have to expect that they are a jerk ready to smack me down if I offer less than 50/50.
Our sense of fairness is anything but rational and this has been supported in animal experiments. de Waal and Brosnan carried out a lovely experiment looking at the sense of fairness in monkeys (macaques, I believe). Two monkeys were in neighboring cages, within sight of each other. In exchange for performing a simple task (a token exchange) they monkeys got a cucumber reward. Both monkeys would do this without hesitation for 20 repetitions. But when one monkey got a grape (a better reward), the one offered the cucumber stopped performing after only a few rounds. That is completely irrational. The cucumber was a fine reward before, but now that monkey 2 gets something better, the cucumber is not enough.
Knowing that and the human desire to “stick it to” someone, I’d go 50/50. It’s got the highest chance of getting some money. The chance of an additional hundred or so isn’t worth the risk of giving up $500.
No kidding. The only value to this poll is to investigate the reasoning of those who chose differently.
There’s a British gameshow based on this sort of idea, called Divided, except there are three people involved in the negotiation, and it goes back and forth rather than being a one-off offer. The way it works is they answer questions to build up a usually quite substantial fund, then three rather unequal shares of that fund are presented to them. They then have 100 seconds to agree on who gets which share. As the clock ticks down, the fund, and therefore the shares, dwindle to zero.
Anyway, stubbornness and pride pay a big part in Divided, and quite often the prize fund drops to zero because they can’t agree. People lose tens of thousands this way.
It depends how well you know the other person (in the game show, they are strangers who don’t meet until they actually start the game). If it were a stranger I’d go for a 50-50 split, $500. Even at $600/$400, I think it’s too risky that the person would say no.
I suppose I’m an “economics person”, given my master’s degree and eventual PhD (er, let’s hope, right?). My answer may be skewed for that reason.
There are a lot of variables at play here—how much do I like this “buddy”? Is he impoverished? Wealthy? I suppose that in general I would choose to keep a some premium for myself above splitting it evenly, enough so that—given the circumstances—he would be sufficiently enticed to take the offer. Clearly that involves leaving him more than $1, an amount very easy to refuse with a “Screw you, guy”. With apologies to ghardester, however, my friend would be a damned fool not to accept a $501/$499 split.
ITR champion: If you have no knowledge of economics, I’d advise you kindly not to spread mischaracterizations of it. “Rational” does not mean “caring only about money”, although it may imply that in very simple examples.
You have a very simplistic view of how economists think.
The basic assumption of economics is that people have various objectives, and that they tend to behave in such a way as to achieve those objectives. That is the economist’s definition of “rational” behaviour. Derived from this is the concept of “revealed preferences”, which says that you can learn something about a person’s objectives by observing their behaviour.
However, economists do not claim to know why a person has certain objectives. That would be a question for a psychologist. If you regularly pay a Dominatrix $500 to whip you on the butt, but you stop going when she raises her price to $600, the economist would just dispassionately observe that the value, to you, of being whipped on the butt is somewhere between $500 and $600.
And no economist has ever claimed that all people have the amassing of as much money as possible as their only objective! (In fact, the only reason why money has any value at all is because you can exchange it for other things, such as food or concert tickets or being whipped on the butt.) The reason why economists talk about money a lot, is because it can be used to achieve many different objectives and it is therefore a convenient measuring stick to compare different people’s objectives against each other.
The topic of this thread is actually game theory, not economics. From a game theory perspective, it is perfectly valid to simply declare “obtain as much money as possible” as the goal of a particular game being analysed, just as “capture the opponent’s King” is the objective of Chess.
Now, when the Ultimatum game is played by real people, we see that the second person does not behave as if obtaining the maximum possible amount of money is his only goal. And we also see that the first person correctly anticipates this. What can we learn from this?
From an economist’s perspective, it confirms that obtaining money is not the player’s only objective. Punishing bad behaviour, or making a positive impression on the other player, is also important. By observing many repetitions of the game, we can even try to measure the average value to people of things like fairness and honesty.
From a game theory perspective, we could conclude that people are playing the game incorrectly, just as a chess player exchanging his Queen for an opponent’s Pawn would be making a bad move in most cases.
However, we could also conclude that the players are behaving as if the game is just one round in an iterated game: by establishing a reputation of fairness (by offering an even split) and of not being a pushover (by refusing an unfair offer), they may be giving up some money in this round, but they may gain a better position in the larger game. As constanze pointed out, even though the ultimatum game is a one-shot deal, human society as a whole could be viewed as a very large and complex iterated game in which players often encounter each other repeatedly, and therefore it makes sense to invest in a good long-term reputation even when you have to sacrifice some short-term gains.
Another problem with this thought* experiment is that you always have either too much** or too little information.
In this case, the motives of the third man - the one who is offering the money in the first place - also play an important part. Who is that man? Why does he go around giving money away? Is the money tainted in any way? (The police will come to your door because it’s drug money or from a bank robbery?) Is he a millionaire, looking for a decent person to appoint a heir, so if you split 1 mio 95 / 5 because 5% is still " a lot", you will loose the bigger fortune? An alien, testing the human species? Maybe it’s a con so the two strangers can see where your wallet is, or they will start charging you. How do you know the man will keep his promise - maybe he’s a psychopath, and the wrong answer he will chop your head off?
Okay, some ideas are a bit farfetched, but still, an average person wouldn’t just accept a stranger offering money split two ways without wondering about it.
The whole scenario reminds me also of the old (Sufi?) fable about two brothers and their inheritance:
A wealthy man had died without a will, leaving two sons who were not in agreement with each other on how to divide the estate. Finally they went to a wise man for help. The eldest argued that he had the right of firstborn to divide. The younger argued that his brother hated him and would screw him. So the wise man said “The elder has the right to divde the estate.” The elder grinned, the younger started to protest. The wise man continued “And the younger has the right to choose first which part to take”. The younger smiled, the elder looked thoughtful.
- I haven’t heard of any game theorists having enough money to play it for real with real people
** In many of the ethical dilemmas, like the life-boat scenario, you know what will happen, which you would not know in real life
That is indeed the common “rational” answer. Why then do so many people opt instead to give up money in order to punish the other party?
I recall reading a anthropologist’s take on the problem (sorry, no cite), and giving up money to punish the other party is actually a rational course of action for a repeated game (or even a single game where others will be made aware of the outcome). In hunter-gatherer days, food was often: (1) perishable, and (2) found in quantities too large for one person to consume. For example, killing an animal or finding a small orchard of soon to spoil fruit. A single person making the kill or finding the fruit often had two options: (1) keep the food secret and gorge him/herself, in which case a portion would likely go bad, or (2) share the food with the tribe, in which case he/she would get a smaller portion (but others would eat, too).
Option (2) is optimal for the long-term survival of the tribe as a whole, even though it may be temporarily sub-optimal for the member making the specific kill or find. So, behavioral norms developed to punish those who were overly greedy. For example, the hunter making the kill might get the choicest “cut” of meat, but the rest would have to be shared. This is similar to the ultimatum game, where the first player often gets away with taking a little more than an equal share as they have the “first player” position. If they get too greedy, though, a message must be sent to them and all other members of society that such behavior will not be tolerated.
Lacking a cite, I cannot comment on the academic rigor of the argument, but intuitively it makes sense.
As the first person: I would offer $1. But, as septimus pointed out, this would only work if that person was rational. If they were irrational, illogical or otherwise retarded, I would have to offer more, possibly up to 100.
As the second person: I am helpless but to accept any offer given by the first person. As the second person, I would actually campaign to be the first person instead.
I’d offer to split it halfway. If we’re being supervised, I want to make myself look good.
As for what I’d accept… I don’t know. Maybe I’d only take half the money as well. Or 60/40. Anything less would be an insult.
In a real-world situation it would depend on how much I liked the other person and what I could get away with without being considered greedy/a thief.
I would offer $1 because I would accept $1. Because $1 is more than zero. It’s very simple if not iterated. I don’t consider it an insult as the second person, because I know the first person is perfectly reasonable in proposing their split. I see no reason why it matters how much the other person is getting; to the second person, the choice is between $1 and nothing. Yes, the situation does style the second person as my “buddy”, but that’s incredibly vague. Most people I’m friends with would understand exactly why I would offer the “rational” split.
However, the amount of money involved in the given scenario is not life changing or even all that significant. While it would hurt having to spend $500 on an unexpected expense, losing the chance at $500 in extra money means practically nothing. When you get into amounts of money where the utility of the money is no longer linearly related to the amount, the more willingly you should be to hedge your bets. Thus, the larger the prize pool, the more I would be willing to offer. If it was on the level of 100 billion, I’d even consider offering 99% of the pool just to make it more likely to be accepted since 1 billion would be more money than I could probably ever spend.
The only reason people view 50/50 as “fair” is the undercurrent of society and the social ramifications of the decision. From my perspective, the second person is just as much in a position to demand he be given the lion’s share as the first person is: don’t give me enough, and I might spurn you just because I feel I deserve more. After all, viewed in the context of society, I might feel I need the money far more than you or I might be able to some way make your life miserable and thus have reason to justify that I should get more of the loot. This is perhaps why the situation postulates the second person as a “buddy” - a supposed equal who should be dealt with fairly. When large amounts of money get involved though, some friends may have different feelings…
I think going for 60/40 would be a pretty big mistake, because if he turns down the offer it will be for reasons of pride, not practical reasons. Too much risk for too little reward. Either go 50/50 or go for a serious edge, somewhere in the 85/15 area. I think the latter is likely to show more profit in the long run, but 50/50 might still be preferable depending on how much you need the money.
Going for 999/1 over 85/15 is a huge mistake, because $1 is trivially easy to turn down for anyone with a shred of self respect.
I offer $1 also because that’s what I’d accept. I’m assuming, though, that it’s a single-iteration game, just as the puzzle is normally set up.
I view it thusly:
The first player is in charge of the money. That’s his money. It’s his right to do with it what he pleases. There is no “fair” offer here. The $1000 belongs to him.
The second player has a “screw you” token. They can play it and ruin player 1’s stash, or take some money.
The ONLY THING that should be considered here is “how much does player 2 value the token?” The only thing player 1 should do is figure out the least amount of money for which he can buy the token. That’s all he needs to offer. If I were player 2, my token is valued at exactly $1. I’d refuse the pocket change because it’s a nuisance, but with $1, I can buy a can of pop. That’s worth the token.
I have no idea where this idea of “50/50 is fair” comes from. What criteria is that based on? How are you coming up with that number? Player 1 pays player 2 to perform a service (surrendering the token). It’s no different than paying for lunch or for an oil change. Does the waiter/mechanic demand to see your bank account and ask for half of it? Would they spit in your food/drain your oil if you refused to give them half of your money?
So where is this 50/50 idea coming from?
You can’t assume your opponent will think the same way you do. For 999/1 to work out better than 50/50 your opponent has to value $1 more than he values screwing over the guy who won’t share the money with him, more than 50% of the time. Chances are he won’t. Most people will see a pithy $1 as an insult knowing the other guy keeps $999 for himself, and be likely to turn down the deal just to fuck you over. I know I would. I don’t need $1. I can buy my own damn can of soda.
Like I said earlier, sometimes people just need to be told to go fuck themselves. Offering $1 to me translates “Fuck you, pal” and refusing the dollar is a “Fuck you, pal” back.
You think that irrational behavior spoils this simple economic theorem, you should examine supply and demand curves and price setting mechanisms.
Many producers will continue to price goods and sell them at a loss for long periods of time even when the rational producer should shut his plant down and reduce the overall supply allowing market pricing to rise due to less supply available. But because of irrational producers, it rarely happens as soon as it should.
Where are you getting these figures? How can you say “Chances are he won’t”? I don’t think that’s true, given the situation I set up, i.e. it’s a one-time interaction amongst strangers that need the money. Chances are they’ll take it.
Why? Why is that offensive? Why aren’t you saying “Thanks a bunch, have a nice day.”? I don’t understand where you’re getting this conclusion that 50/50 is fair and any less is a “fuck you, pal.” Offering $0 is a fuck-you, not $1.
I didn’t say anything less than $500 is a “Fuck you.” I said $1 is a fuck you. I’d gladly take $400, though I’d grumble beneath my breath, “You greedy little…” but as the amount offered is lowered, the louder the grumble gets, before I ultimately decided to just stiff the bastard. I won’t give an exact cutoff, because once I do someone will go “So you’ll take $200? How about $199?” but $1 is definitely well below my threshold.