Ultimatum Ruminations

Jick’s comment on yesterday’s post meshes well with recent discussion of fairness. Let me introduce you to the Ultimatum Game, a favorite of experimental economics. There is a pot of money; player one allocates it, as much as he likes for himself, the rest for player two; player two chooses to accept this (and they both take their money) or reject it (and both get nothing). That is it.

Simple economic rationality suggests that you take whatever is offered: free money. In practice, people will start turning down free money if it means the person making the offer gets a much larger piece of the pie, with most people bailing in the one-third to one-fifth range. In the vernacular, screw that jerk.

That would be my translation of Jick’s comment as well: screw that jerk who bid $1 over the other The Price is Right player. Just because the rules let you do something does not mean that it is fair. Of course, the English word fair is a horrible mess. English speakers mash a dozen concepts into the word and equivocate madly. Does fairness mean playing by the rules? An equal outcome? An outcome that satisfies the most people? An outcome that rewards people based on their inputs? If asked to pin down a definition, many people will pull another vague term like “equitable,” which has the same problem. Bart Wilson has been trying to work that out.

I am not criticizing Jick’s point. I do not agree with it, because I think competitors in a game environment should do anything within the rules to win, but it is a viable social norm. Are there conditions under which you should not really try to win? Let us explore a few variations on Ultimatum below the break.

First, what if it is not a game? The experimenters offer you $4. No game, no catch, would you like $4? If so, take the money. If not, leave it. Any reason not to take it?

Second case, what if you do not know how much is being divided. You are offered $4. You might assume that it is a $10 pool, being offered 60-40, but for all you know it could be a $100 pool being offered 96-4. The experimenters probably do not have that much money lying around for 10 second games. You probably assume a $10 pool and take your $4.

What if you do not know which is the case? You are offered $2. You may or may not be playing Ultimatum, and if so you do not know the pool size. Do you accept the free money if there is some risk that someone else is walking away with $8, or $98, or maybe just $2 from a $4 pool?

In these cases, I have assumed anonymity. I do not have experimental results handy, but I would bet that you get different results from different conditions. Completely anonymous, met once at the start of the experiment, or someone you previously knew? In separate rooms, by computer, visible to each other through a window, separated by a screen (but still audible), or seated at the same table?

More interestingly, you can have repeated games. Do you play differently if you know that there will be 20 repeated games? If there will be an unknown number of repeated games? If you reject $3 in game 1, you will be more likely to get $4+ in game 2. Might you reject $5 in game 1, if you think you can get $6 and the offerer will accept $4 rather than $0?

Or reverse all of those and think of what you might offer.

Dictator takes the opposite extreme of the first case I said. Player one divides the pool. Done. There is no accept/reject, just how the first player chooses to divide the money. He can take it all. He can split it all. Player two just watches. Again, I would bet on different results if player two is an anonymous player in another room.

If player two is anonymous and in another room, would you believe that he exists? You were told that you were taking part in an economic experiment on what people consider fair, but psychological experiments frequently lie to participants. You might just be turning down free money, offering it to no one. Even if player two is in the same room, he might be a graduate student working for the experimenter, with the money going back into the research pot.

Have I instilled doubt? After doing so, what would I need to do as an experimenter to reassure you that there really is another player in this experiment, rather than one of my confederates?

What if you are player two, and I tell you that player one is working from a script. He will be dividing the pot of money each time for ten games, according to what the page in front of him tells him to do. Would you still reject an unfair offer if he had no choice in what to offer? If so, how does this differ from that first case where I just offered you money? Does it matter if player one is another player, who will get the money or not, or another researcher who will not keep the money himself?

Does scale matter? You are offered $300 from a $1000 pool. Would you turn that down? $3000 from $10,000? Wikipedia says that Indonesian players have turned down two weeks’ wages when offered in a 70-30 split. How about $100,000 from $1,000,000, where the other player walks away with $900,000?

For my last bit of pondering when you will reject free money, consider the game with multiple players (the Wikipedia link at the top has some of these variations). You are one of three players offering to divide $10, and “player two” will pick one of the three; the other two offerers get nothing. How much are you willing to offer to out-bid the other two? Is there a point at which you say, “screw that jerk,” for the person choosing between offers? What if you really are bidding, and you can change your offer (repeatedly) after seeing the others? You might quickly get to offering $9 and change to walk away with anything.

Thoughts, variations? It is a very simple game, but you can see the many ways that little changes can affect the outcome. It is intellectual play day at Kill Ten Rats.

: Zubon

9 thoughts on “Ultimatum Ruminations”

  1. There’s also the question of whether a game is competitive or cooperative and people get so used to being the jerk that screws others that they still do so in cooperative environments. Human nature, competitive culture and all that.

    I know that I often jump into these games with the naive thought that in escaping the real world, I might escape some of these trappings that come with it.

    There’s probably a little game theory involved here, but my brain hurts too much to work it out at the moment.

  2. There’s also the question of how you’re being observed. I expect neurotypical people would find the 1201 USD bid a lot more acceptable in a free money environment, over an environment based on an IQ test, over an environment with dropped money, over an environment where they’re being asked about fairness, over an environment where they’d be seen as being ‘unfair’ on television. (That’s only really accurate for neurotypicals; schizoids are less sensitive to observation bias, and those with antisocial personality disorders are a lot more unpredictable).

  3. Once again displaying neurotypical bias, I had not even thought of how the game might go with autistic players or others on the spectrum. Sociopaths could be interesting. I would also like to see the poster at the university advertising for sociopaths to play an economic game.

    Feel free to insert a joke about economists and sociopaths.

  4. The problem they have with taking the money is they feel they are rewarding the person who is keeping 80% of it. Maybe they are not thinking about it in those terms, but maybe figure if they don’t reward behavior they disapprove of then the other person will think twice about engaging in that behavior in the future. But in his head he’s just thinking “screw that jerk”

    It’s funny since then who is being nice and who is being selfish? One is offering the other money, the other is saying he’d rather both players be poorer than get less, and patting himself on the back for his advanced morality.

    It would be interesting to see an iterative version, where maybe each person takes turns. The “selfish” player might keep on dividing it 80/20 and the “nice” player 50/50, how many iterations would this keep going before the “nice” player either gives up and takes the 20%, or else decides to split it 20/80. And what does that mean.

    Ever since I started studying game theory even at my dilletant level I have thought everyone should study it.

  5. “I know that I often jump into these games with the naive thought that in escaping the real world, I might escape some of these trappings that come with it.”

    I know what you mean, that damn real world gets harder and harder to escape! I really am not a people person to begin with, then I play MMOs. Probably not a smart move on my part.

  6. I had fun with this last night with my very sweet wife. I told her the premise of the game using a $100 pool and I said I would give her $20. She responded she would always take because more money is more money. Then I said what if I gave her $1… the reaction was pretty funny.

    I think this is very interesting especially in terms of WAR’s guild tax. It’s not the same premise, but it is very close.

  7. “Feel free to insert a joke about economists and sociopaths.”

    Those are two different groups?

    Will the IRS see this “free money” as income? Is it hot off the printing press, money from a research grant, or just monopoly money?

    …is it in small, unmarked bills?

  8. In Chicago today at the American Association for the Advancement of Science meetings this week: Frans de Waal presented a similar game with Chimps: chimps were given cucumbers after performing a task. When after awhile one chimp was given grapes afterwards instead, the other cucumber chimp went ballistic, throwing his food away and refusing to do the task.

    Somewhat similar idea. The chimp wanted the same reward for the same effort.

    They also found that when they gave the chimp the grape for nothing, he also refused to do the task, just demanded the grape.

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