The ultimatum game played by children

I came across a cute video about game theory.

The video is about an experiment where children are asked to share a pile of chocolate coins. The twist to is they had to follow the rules of the ultimatum game.

Specifically, here is how the game worked. One child got to offer a split of the chocolate (“9 pieces for me, 1 for you”). Then, the other child could either accept the split and take the candy. Or, she could reject the split and both would go home empty-handed.

What should happen? Game theory predicts the proposer has the advantage. In theory, the second player–the one hearing the proposal–should be favorable to most offers. The reason is that rejecting an proposal leads to a zero payout. It is better to get something rather than nothing, so the second player is likely to accept most offers even if she ends up with little. Consequently, the proposer can make almost any offer and will make one that gives him most of the chocolate. In effect, the proposer can make an ultimatum which the second player will find hard to refuse.

Of course, the game does not always works so smoothly in practice. How do the children play this game? Watch this entertaining video on youtube to find out:

Link to youtube video: the ultimatum game

*I am in the dark about the show. I would be very grateful to anyone that can identify the source of this show/experiment.

My video transcription

Narrator: In this experiment, seven and eight year olds are sharing a stash of ten chocolate coins. One child decides on how they are split, and they can offer as many or as few coins as they like.

Children in experiment: [offer various splits from one to three coins]

Narrator: At first they keep more for themselves. But there is a catch. It is the other child who gets to decide if the split is fair. If not, they can refuse the offer. And then, both children have to go away empty-handed. Will they get away with it?

Children in experiment: [almost all reject small offers]

Child 1: What do you mean [you reject]? That means you don’t get any chocolate!

Child 2: I don’t care. It’s already too little.

Narrator: Almost all of the children reject the smaller share, preferring to have nothing at all. It may seem strange, but it is not. By going without themselves, they are punishing their partner who loses even more chocolate. And they are not going to forget that in a hurry. Look what happens when the experiment is repeated.

Children in experiment: [most offer nearly even split]

Narrator: Now, with a fairer split, what will the response be?

Children in experiment: [most accept nearly even split]

Narrator: The children are happy to accept. It is not difficult to see why we have evolved this way. If we react instinctively against people who cheat, they will think twice before trying it again. And it has left us all with a taste of fairness.

This video raises many interesting questions. Here are a few thoughts that came across my mind:

What game are we playing?

In the first round, many of the children give small offers which are rejected. This comes as a surprise to many of the proposers. Why might this happen? It appears the receiver of the offer gets almost no satisfaction from the pittance of an offering. Instead the receiver gets joy from rejecting the offer and punishing. The lesson? The children are playing a larger game. The ultimatum game is not wrong, per se, but it is obvious the children are not playing it. They are instead playing the game of “I want candy, but if you are not fair I will be more than happy to punish you.” And it is the very fact that they change the game that alters the outcome.

Repeated play changes the game

Repeated games can have very different outcomes from one-shot games. In a one-shot ultimatum, one would fully expect low offers to be accepted. But not so in a repeated game. In this experiment, the children likely do better by rejecting the offer in the first game and getting an even split in the second (netting say 5 chips) than they would have been by accepting two sets of low offers (netting say 2 chips).

Fairness is very important in division

It is not always easy to say what is fair. But it is often the case we know what is unfair. Fair division is a topic that comes up time and again, in splitting bills, determining homeowner fees, and even in eating peanut butter and jelly sandwiches.

The children are obviously concerned with a fair split which affects the outcome and prevents the offerer from making unreasonable ultimatums.

Discussion questions

1. How might the game change if the children played with other foods like vegetables or slices of pizza? Or money?

2. Do you think the children knew the game would be repeated?

3. Would the outcome be different if the children switched partners between the first and second games?

4. How would the game be different if the recipient could give a counter-offer? [this is sometimes called the double ultimatum game]

5. Comment on how this experiment is similar to the song “Before He Cheats” by Carrie Underwood [video on youtube]

6. Offers to the ultimatum game vary worldwide. Summarize some of the differences as summarized in Tom Siegfried’s article “Social Thermometers” in The Dallas Morning News [link to article - .doc file]



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  • Hari

    Hey Presh

    Hope all is going well.

    So, I read your post, here’s my thoughts.
    1) With items like vegetables, its possible the offer will be the opposite (kid offering to give them all away) in many cases. It might or might not be accepted, depends if the recipient can toss them or has to eat them.

    2) Can’t say. Kids are taught to value fairness, so their utility function is probably increasing in candy and in fairness.

    3) Do you mean if the recipient had a chance to offer? I think they would probably do the same thing (offer something unfair) to get even. If it were adults instead of kids… it might be different.

    4) Hmm. The second offer should be just like the first one in the original game. I.e., now the second player has all the power. But, if the first person offered “I’ll give you 4″ the second player might want to reciprocate the relative fairness by offering the same back.

    5) Neat analogy, but not perfect. In both cases, one person (recipient or Carrie) cares about some sense of “the world being good” as part of their utility function. However, with the game, when the recipient turns things down, they are losing something. But, in the case of the Carrie Underwood song, I imagine she’s going to break up with him anyway, and the destroying the car makes her feel good, so there is no sacrifice to go along with improving the world (legal action aside… which I imagine seems unlikely from the video, but maybe not…).

    To me, overall, there is no mystery. The fact of the matter is that the kids care about more than just chocolate. Its like people wanting to use the prisoner’s dilemma in real life on prisoner’s. They care about more than just jail time (i.e. pissing off their partner who might come find them after). However, games like this are neat and useful in finding out what people care about.

    Finally, a side note…

    Lets say this game were played with adults but instead of chocolate, it was bags each containing $100,000,000 (where the bags can’t be divided up). Well, then most people would take the one bag since in this case their sense of fairness is outweighed by the awesomeness of just one bag.

    - Hari

  • Scott

    1. I think it’s clear that the actual object doesn’t matter. It’s the relationship between the what the proposer gets versus the receiver.

    2. No, and this is what I feel is the most interesting part: that we’ve evolved to have this innate sense of the bigger picture. It’s not that we know ahead of time that the games will be repeated, it’s the fact that the games are, infact, repeated and those that treat each game as if it will be repeated will win out over those that treat each game as an isolated event.

    Let’s say we’re talking about food. If the individuals treat the game as repeated, then both will get an approximately equal amount and be fed. If they treat the game an isolated event, then they both get nothing and starve. In the end, all that remain will be those that treat it as a repeated game, regardless of whether or not they consciously know it will be repeated.

    3. Good question. I would say yes. The initial game shows that the proposer will be greedy if he thinks he can get away with it. The result shows that he can’t get away with it, so he is more fair the second time. By changing the partner, the proposer is likely to try and be greedy again, since there is the possibility this new receiver will fall for it.

    4. I think counter-offers would be more favorable to the receiver. If left entirely to the proposer, they will most likely choose a pairing that still favors them, but is good enough for the receiver that they accept. Counter-offers remove this advantage.

  • Bryan

    What I saw in the video was exactly what I expected to happen, and what I myself would have done (even if the content was bags of $100000000 dollars). The reason being that if they didn’t offer me a reasonably fair share, they stood to lose a lot more than me. I might lose 1 chocolate, but they lost 9 chocolates, which is much more painful.

    Game Theory makes the assumption of _rational_ players, but I’ve found that a lot of decisions made by real people are not rational.
    It also presupposes that games operate in a vacuum, which as seen in this case, they really don’t. In this case the opportunity to punish the unfair person was more important than the small payoff.

  • http://wjspaniel.wordpress.com William Spaniel

    The setting–a classroom–and the interaction between the children leads me to believe that they all knew each other before the games were played. Perhaps they are classmates. That being the case, the ultimatum game doesn’t really fit the situation. Even after the video is turned off, the kids are going to be interacting with each other. And in such a repeated interaction, as the above comments have said, punishing defection is extremely important.

    Axelrod, you never fail me.

  • Gamer

    I find it funny that the kids even gave the other child ONE chocolate, if they were greedy then they would have taken all the chocolate and shared none. The offer of even one chocolate means the kid expected the other to accept the offer.

    1) …hmm a game using items they didn’t like? Because if they didn’t like it then the offer is player 2 gets all of it, then player 2 refuses and both avoid receiving the unwanted item. If the situation is that it is an unwanted item and if the offer is refused then both receive the total (the sum of both shares) then I think the game would play out the same with children (offering the other more of the unwanted). When adults play it I believe that their response would differ then the normal ultimatum game (they would offer an equal share hoping to receive less than the punishment of refusal).

    2) I don’t know, but I think they believed it would end in one round since I think that their offers were more “You do know you’ll get nothing if you refuse right?” rather than “let’s see how low the other person will go.” based on the fact that in the second round they offered almost even instead of one more chocolate than last time.

    3) It would be different, they would offer a small amount to the other again. They only know that the previous person will definitely refuse unfairness but they can still try to maximize chocolate with the new person.

    4) Both children would offer a smaller share to the other, and both proposals would be refused (and even if the first offer was fair it would be refused).

    5) The reactions are pretty much the same: Defecting is being unfair and Punishment is refusal. Also the results of the previous event dictate the next set of actions. I just find it different in the thought processes.

    Since they are children I think that they are only looking to maximize their gain (even the one who accepts/declines). Meaning that if they were in a game where the proposer has only two options: 100 chocolate for p1 and 10 chocolate for p2 or 5 chocolate for both, the acceptor/decliner would agree to the first option instead of the last one (while an adult would find that unfair and accept only the latter). I think they only accepted the fair offer because they think that’s as much as they can get (same line of thinking as answer to 4).

  • Jimmy

    @Bryan:

    Game theory only supposes what SHOULD happen, not what must happen. It is there merely to predict behavior not encourage it.

    This game is difficult use as any sort of predictor of behavior as humans are funny creatures when it comes to vengefulness (is that even a word?). While it’s easy to say you would reject the 1 piece of candy (which is irrational…but that’s besides the point), I have a very hard time believing that you would turn down $100,000,000 when you partner is getting $900,000,000. Clearly, the split is uneven, but the gains of accepting, financial freedom for life, HAVE to outweigh the gains of rejecting, satisfaction in knowing someone else didn’t get more than you.

    The interesting thing I found with this test is the idea of fairness. Honestly, is it really ‘unfair’ for someone to get 1 piece and someone else to get 9. The logic obviously dictates that if you start with nothing and can get something then it’s ‘better,’ but is getting less than someone else in the same position truly unfair?

  • Hari

    @Bryan

    Certainly, this argument assumes rationality, but it would be wrong to say that all game theory assumes rationality. There are people studying “bounded rationality” where other assumptions about reasoning are made.

    However, I don’t think thats the problem with this argument. Rationality merely means that one acts to maximize happiness. In this case, happiness is based on a sense of fairness or envy. In these situations, it is in fact rational to reject the 1/9 split.

    So, the question is, how much does fairness/envy matter to each individual. As per your statement, it seems to matter to you a lot, far more than it matters to me. I would take the 1 bag no matter how unfair it is. But that doesn’t make either one of us more or less rational (though, some people might argue that one of us is more reasonable).

    Its important not to confuse the way game theorists/economists use the word rational with way its usually used.

  • David

    This behavior about seeking fairness is actually cultural not evolutionary despite the commentary on the video. “In Sway: The Irresistible Pull of Irrational Behavior” by the Brafman’s. The authors discuss this experiment, as it is replayed in different countries around the world. Specifical natives in the Amazon would be fine with the 1/9 split because they would consider any gift as being better than where they were before. This concept of fairness is western in origin.

  • Mauricio

    Another demonstration of the tit-for-tat strategy in action.

    Tit-for-tat is usually associated with the iterated prisoner’s dilemma game. Nice to see it working in other games too.

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  • bob

    Maybe they’re just punishing them for greed. I would too (I don’t especially like chocolate.)

  • http://www.nmfaf.org Vincenzo Hospelhorn

    My Firefox stopped working saying the server wasn’t found but Internet Explorers still works. I used to use firefox all the time but only recently it stopped working. I already checked the firewall and it allows firefox so i don’t know what’s wrong..

  • http://www.mindyourdecisions.com/blog/ Presh Talwalkar

    Thanks for letting me know Vincenzo. I tried it in my Firefox browser and it was working, so I’m not sure what was wrong, but I’ll look into it. Thanks!

  • john

    Scott seems to be the only one who realizes that “revenge” for being treated “unfairly” IS rational from a game theory standpoint. Presh points out how it is rational for a repeated game, but not for a single game.

    The problem with the single game solution, is that it implicitly assumes life ends at the end of the game (or alternatively that people have no memory or some other equally unreasonable assumption). But life doesn’t end.

    Anyone who doesn’t defend their right to be treated fairly will be marked as a target by anyone looking to take advantage of someone. The long term payoff of “revenge” isn’t just the pleasure it gives as many suggest (and call it irrational – while technically it is emotional and not rational, it does have a rational purpose). The long term physical rewards(cash, food etc. – from being treated fairly in the future) should be much greater than the loss. That is the reason we have such a strong sense of “fairness” (see Mel Gibson’s “Payback” for an extreem case – but only if you can handle violence).

    David suggests the concept of fairness is western. I strongly doubt that to be true. However different cultures have quite different ideas about what is fair, and hence the game will play out differently for each notion of fairness.

    Even monkeys and apes appear to have a fairly well developed sense of fairness. I don’t have the links right now, but a search for “monkeys fair play” on Youtube should get something.

    If we’re dealing with bags worth 100M each, then accepting 1 bag out of 10 becomes rational for 2 reasons.

    1st, Presh points out in another post that the more money you have, the less it means. 100M is more than most people would spend in a lifetime, so who cares about the rest (OK, most people would care, but for most – those who aren’t already filthy rich – the 100M would be worth more than the extra 800M)

    2nd, the single game solution is more relevant, as it is highly unlikely that future gains would ever amount to 100M.

  • http://gametheory101.com William Spaniel

    There is nothing irrational about rejecting offers. Anyone who says this–and plenty of economists do–have no understanding of rationality or expected utility theory.

    http://www.youtube.com/watch?v=6E5eRAlOCvc

  • http://gametheory101.com William Spaniel

    And, for the record, I meant that independently of whether this is a one-shot or a repeated game.

  • Mauricio

    You guys might want to read this:
    “Raising the stakes in the ultimatum game: Experimental evidence from Indonesia” – http://www.econ.ku.dk/tyran/Teaching/BEecon_MA/readings_BEecon/readings%20MA_Expecon/Cameron_Indonesia_EcInquiry1999.pdf

    The results show that raising the stakes does increase the acceptance of offers, but at the same time, diminishes the amount of unfair offers.
    At high stakes, fairness starts coming from the proposers.

    Although the theory says at high stakes the acceptance of unfair offers should be higher, the proposers are not willing to risk losing everything to find out if it is really true.

    The hardcore fairness from a few stubborn responders is powerful enough to trigger fairness from the greedy proposers. Nice huh?

    Important note, the experiment was conducted in the “one-shot” way.

  • john

    Mauricio’s experiment does not seem very surprising.

    My first reason for accepting the “unfair” offer in the high stakes game would also be a reason to make a fair offer in that game.

    There is also the fact that we are dealing with people who aren’t always rational, and whose motives aren’t necessarily only material in nature (so even if they are completely rational, they won’t necessarily try to maximize their material gains).

    For those debating rationality, which is more rational: accumulating all the material wealth possible and then fretting over it’s possible loss, or forgoing all unnecessary material wealth and living a peacefull contented life? I think all game theory problems I’ve seen assume all rational beings would pick the first.

    P.S. Sorry William Spaniel, I somehow missed that you also understand that rejecting offers has utility and can be rational.

  • Mauricio

    The catch with rationality and game theory is,
    even if people act rationally as individuals, as a group their combined actions can still be irrational. What game theory does is prove that.

    What is the ultimatum game? It is a game theory model which proves that rationality can lead to unfairness and people end up getting hurt.

    Rationality is overrated. This is the most important lesson game theory taught me and, sadly, most game theory articles miss this point entirely.

    I wish I had William Spaniel video editing skills, so I could teach this to everyone through You Tube.





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