Income Inequality and Game Theory

Consider this situation:  You are a member of a four-person rock band.  Each member of the band has contributed somewhat equally over time, and band revenues have always been split evenly, 25% to each member, though its total earnings on an absolute basis have been small  However, the band has suddenly become the next U2.  It is likely the band will make tens of millions of dollars over the coming years.  Just as this is happening, the other three band members come to you and threaten to make you Pete Best.  They will allow you to stay with the band, but only if you accept a reduction in your share of the earnings to 10%.  You perceive this move as unfair given your equal contribution to the band to date.  However, even 10% of the band's new fortunes would be a LOT of money (and fame) and you honestly believe that even a 10% share is better than you could do with any other band or occupation.  What do you do -- take 10% or quit?  (assume you want to be famous and you have no legal recourse against the other members)

In an analytical vacuum, one might predict that any rational person would take the deal -- while it is less than might be hoped, it is certainly a better deal than one could get any place else.  A pure profit maximizing decision would be to stay with the band (and watch you back at night for more knives).

However, numerous studies and surveys have shown that in fact, a  large number of people would choose to give up the money rather than feel cheated.  Just look at the number of professional football players who have held out for a whole season to try to get a better contract.  In every case, the present value of the salary lost for that season is far greater than any increase in salary in the future from taking the tough stand.  But these players would rather be paid nothing than feel underpaid.

TJIC had a pointer to an interesting article on game theory.  In it, the author talks about this behavior in the context of a game that divides up pies, and summarizes:

Apparently, making money is not the players' only concern; participants have a sense of pride and care about how they are treated by others, economists have concluded. Thus, offers perceived to be "unfair" are rejected out of a desire for revenge.

In fact, revenge and/or envy has been tested in a number of games, where scientists gave players trailing in the game the ability to spend money solely to take away money from the leading players  (e.g. you can spend your last $10 to make $10 of your opponents money disappear).  There is something in human behavior that wants to bring down the winners, even when doing so makes one worse off himself.  (Question to Red Sox fans:  would you accept a lifetime bad of the Sox from the World Series if you were guaranteed the Yankees would never make the World Series either?)

I guess I don't really have a problem with such behavior in consensual transactions (though I personally work pretty hard to purge my ego from business decisions).  My problem comes when people motivated in this way vote in our society that has proven to have inadequate protections of the minority, at least when we refer to the minority of rich and successful

In Closing of the American Mind,  Allan Bloom tells the story of a question he used to ask his classes vis a vis income inequality.  He would ask something like "Would you vote for a law that reduced income inequality but at the same time reduced total wealth, such that the poor might get a larger slice of a smaller pie, and might even be worse off on an absolute basis afterwards."  Apparently, he would get solid majorities for "yes" and in fact I have been in classes where this same question was asked and at least 40% said "yes."  This is a situation a bit similar to the one above, but without it being personal.  In other words, no one has explicitly hosed you, they have just done better.

I hope you can see the parallel.  Large numbers of people are willing to pay (or equivalently make less money) to reduce the earnings of people who are wealthy and/or successful. They are even  more willing to do so if they think that they have been treated unfairly.  Which is why you see so many politicians and media outlets working so hard right now to convince the middle class that current income distribution patterns are somehow "unfair."  Politicians are pandering to this base human emotion, the desire to spitefully bring someone else down (in the case of income equality laws, someone the person has likely never even met or transacted with) even if it makes oneself worse off.   

I can understand why Pete Best might harbor a grudge against the Beatles.  But why do so many Americans harbor a grudge against people they have never met, just because they make more money?


  1. Jim Collins:

    Several years ago a large steel fabrication plant in my town went out of business. A few days after it closed I was at the employment office and ran into a person who I knew had worked as a welder at the plant. I told him about a job posting I had seen for a welder. We went over to the board and found the posting. He was completely qualified for the position, but the job only paid about $13 an hour. He told me that it was beneath him to work for that amount. Then he got into the line to sign up for unemployment.

  2. Don Lloyd:

    Although the experiment participants are almost certainly unaware of it, in the real world reducing the wealth and income of enough others DOES increase the share of available consumption goods that you are able to bid away from them.

    Regards, Don

  3. Matthew:

    This happens more often than you'd care to imagine. Something like this happened to our band when we got called to play for a major gig. In our 6-man band, our second guitarist was told to take a hike so that each of us get more $$$. Our singer was the one who got us the contract so he decided he would call the shots. We didn't have a manager at the time. When this happened, me and our drummer also stepped down, and offered our share of the money to our badass singer dude, who now had to run the show minus his drummer and two guitarists. Needless to say, the show never happened and we were rid of a parasite of a singer.

  4. Sam:

    Unless I was the lead singer, I would take the cut.

  5. Sam:

    Unless I was the lead singer, I would take the cut.

  6. markm:

    Don: Wrong. It might work if you ate fruit from wild fruit trees, dressed yourself in leaves decorated with pretty rocks picked up off the beach, lived in a cave, and had nothing else you wanted. Reducing other's "wealth" would mean more fruit, leaves, mud, and shiny rocks for you. (But how are you going to keep the others from going out and picking these things up - kill them?)

    But in the real world that we live in, we don't just find ready to use items out in the wild. Apples come from orchards, planted, tended, picked, sorted, shipped, and sold by other people, who expect to get compensated for their efforts. Cut back their share, they won't see a reason to work as hard or to contribute their money as capital to buy land, seedlings, trucks, stores, etc, so there just won't be as many apples available anymore. This is even more true for manufactured goods. Reducing inequality makes everyone poorer.

    Not that real-world efforts to reduce inequality actually reduce inequality. Instead, they replace the rich (who have for the most part become rich by providing things that others want enough to pay well for them), with the government officials who now have the power to take what you earned and give it to someone else - someone who helped them achieve and hold that power, and who doesn't complain much about the part that sticks to the officials' hands. Top party officials get luxury dachas for their vacations, ordinary people wait in line for a short food ration. You replace people voluntarily cooperating for an agreed-upon share of the goodies with the use of force to take the goodies, and hand part of them back as a reward to supporters of the winning party. And since people lose their motivation to work under such a system, not only does it impoverish everyone, but the rulers sooner or later will be using whips or threats of sending people to concentration camps to get the even the minimum requirement of work done.

  7. Noumenon:

    He was completely qualified for the position, but the job only paid about $13 an hour. He told me that it was beneath him to work for that amount. Then he got into the line to sign up for unemployment.

    It's dumb to take any job you're qualified for (I should know; I went straight from college to forklift driving). Homo economicus would hold out for a job that wouldn't torpedo his chances for getting back to $20 an hour by making him look low rent. But regular people are not Homo economicus and they tend to live paycheck to paycheck. If unemployment can counter this tendency by tiding this guy over until he finds his proper place in the economy, it actually would make the system more efficient at getting the right people in the right jobs.

    ps: markm, very persuasive post that I had to think about for a while.

  8. DryaUnda:

    I think a lot of this has to do with fears of the rich hoarding all the wealth. I kind-of touch upon this here: