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More On Golden Balls, And The Best Lesson In Game Theory Ever…

April 21st, 2012 · 12 Comments
Follow Ups · Game Theory

The Prisoners’ Dilemma is a classic problem in economics with a clear theoretical outcome of non-cooperation. In practice, however, people are sometimes “nicer” than economists predict…and apparently this makes the game interesting enough to make a game show about. (Yes, I have been fascinated by this for going on two and a half years now.)

The game show is called Golden Balls (hehe), and the game is called Split or Steal. The setup is pretty simple- there is a pool of money, and each of the two players chooses either split or steal. Furthermore, the two players reveal their strategies at the same time. If both players choose split, then they, not surprisingly, split the pot evenly. If one chooses split and the other chooses steal, the stealer gets the whole pot. If both choose steal, no one gets anything. In other words, this:

This is the classic Prisoners’ Dilemma with one minor twist in that if one player plays steal, it (rationally) doesn’t matter to the other player whether he chooses split or steal, since he gets nothing either way. (This is going to turn out to be quite an interesting feature.) So what would you do in this situation if you could talk to the other player before you choose strategies?

Clearly, your goal is to get the other person to play split, since that is the only way that you are going to get any money. Personally, my initial idea was to convince the other person that I was going to play steal and that he wasn’t going to get anything either way but could come off looking like the good guy if he tried to split.

So why would this work? First off, trying to convince the other person that you’re going to split should be a non starter, for two reasons. First, the steal strategy (weakly) dominates the split strategy- if you think the other player is going to split, it’s clearly better to steal, and if you think the other player is going to steal, stealing is just as good as splitting. This means that convincing the other person that you are going to split is an uphill battle because the other person can see that splitting isn’t in your best interest. Second, even if you can convince the other player to split, all that does is give the other player a greater incentive to steal.

Given this, the only reasonable options are to either not promise anything or to convince the other person that you are going to steal. It shouldn’t be hard to convince the other person that you are going to steal, since stealing is in your best interest. (I would probably explain to the other guy why stealing was in my best interest in order to build credibility.) If he is convinced that you are going to steal, the other person should be (rationally) indifferent between splitting and stealing, since he doesn’t get any money either way. (Yes, I get that there might be a psychological incentive to punish, but that isn’t “rational” from an economic perspective.) Therefore, all you should have to do is provide some incentive to tip the scale towards split for the other guy. What’s interesting is that the other person doesn’t have to fully trust you for it to work, they just have to believe that there is some positive probably the the incentive will come to fruition.

So what actually happened?

As an economist, I don’t think this is weird at all, and I am both shocked and not shocked that this doesn’t happen more often. Perhaps somebody should hire this guy into an economics department.

Tags: Follow Ups · Game Theory

12 responses so far ↓

  • 1 Bill // Apr 21, 2012 at 7:11 pm

    Very clever…thanks for highlighting. Similar to winning in the game of chicken…just cut off the steering wheel, hold it out the window, and convince your opponent you cant swerve.

  • 2 econgirl // Apr 21, 2012 at 8:18 pm

    I believe the technical term you are looking for is “credible commitment.” 🙂

  • 3 Joe Colucci // Apr 21, 2012 at 9:01 pm

    Perhaps a more credible commitment: don’t look at the balls, so they know that you don’t know what you’re playing. Promise to give them half, so they can guarantee themselves half of the money by playing split and hope that they’re risk-averse enough not to try to win it all.

  • 4 Nathanael Snow // Apr 21, 2012 at 9:45 pm

    Better yet, let them chose your ball randomly, making their best strategy “split”

  • 5 Brian // Apr 21, 2012 at 11:28 pm

    Wonderful! I would say that the key here is “belief” – one player truly believed the other would choose “steal”, therefore the only option they believed for them was “split”. The other player also believed his opponent would choose “split”. Anyhow, that’s what I “believe”!

  • 6 Punditus Maximus // Apr 22, 2012 at 10:13 am

    There is a word for someone who has a utility function with zero altruism — “sociopath”. It amazes me that Economics has still not realized that the assumption of rationality is prescriptive, not descriptive, no matter how many times that assumption is shown empirically to be not only false, but impossible to run a society if it were not false.

    Heck, Economics itself, obsessed as it is with Social Welfare Functions, is a violation of said assumption. This has to be unique among scientists and social scientists; sociologists don’t assume that they themselves have no group identities, and physicists rarely assume themselves immune to gravity.

  • 7 Jay Wetmore // Apr 22, 2012 at 12:17 pm

    No discussion of the Prisoners’ Dilemma is complete without referencing Robert Axelrod’s work on iterative Prisoners’ Dilemma games where “nice” strategies dominate.

    Another factor to address (since we are talking about behavioral economics) is that reputation is important to people. Being on national TV, presumably viewed by millions of people, seems a good way to develop a reputation. Which reputation do you want, a ruthless cheater, or a cooperative and fair person?

    Most people will avoid ruthless cheaters whenever they can.

  • 8 RM // Apr 22, 2012 at 11:04 pm

    you were a day late for splitting pot.

  • 9 on line courses | Pearltrees // Apr 23, 2012 at 12:51 am

    […] More On Golden Balls, And The Best Lesson In Game Theory Ever… So why would this work? First off, trying to convince the other person that you’re going to split should be a non starter, for two reasons. First, the steal strategy (weakly) dominates the split strategy- if you think the other player is going to split, it’s clearly better to steal, and if you think the other player is going to steal, stealing is just as good as splitting. […]

  • 10 SBarnes // May 3, 2012 at 5:06 pm

    Take out a checkbook and write your opponent a check for 50% on the condition that they chose ‘split’, then declare that you are playing steal.

    If they screw you, you have a video-tape of the verbal agreement (nullifying your commitment to them).

  • 11 Hassan // May 2, 2013 at 1:17 pm

    Hi jasper thank you for updating this it really makes me laugh when they argue but then at the end they both SPLIT.

  • 12 Golden Balls game and game theory | kirikkomori // Nov 6, 2013 at 12:37 pm

    […] http://www.economistsdoitwithmodels.com/2012/04/21/more-on-golden-balls-and-the-best-lesson-in-game-… […]

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