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A Lesson In Game Theory (And Golden Balls)…

October 27th, 2009 · 10 Comments
Game Theory · Videos

As a math geek, I have a particular fascination with game theory. Lest the word “theory” through you for a loop, keep in mind that game theory has a number of practical applications. In general, it’s useful in life to be able to think about how others are going to respond to the choices that you make, since these responses in part dictate what choices are best for you to make in the first place.

To illustrate this concept of strategic interaction, I give you a couple of videos. The first goes through the typical prisoners’ dilemma setup, and the second gives an example of a second type of game that has a lot of instances in the real world.

I swear I have an entertaining point here, but it requires this sort of game theory knowledge. So just bear with me…

Ok then. Now that we’re up to speed…you may have noticed that game theory is a bit out of order in the context of the production of my Econ 101 videos. So what brought this on? Well…The Economist reminded me of a particularly intriguing British game show called Golden Balls (not to be confused with David Beckham). I had previously thought that my fascination with British television was limited to Monty Python, AbFab, The Office and Trinny and Susannah’s version of What Not to Wear, but apparently I was mistaken. The show has a number of different games, but the most economically interesting is the “Split or Steal” segment, since it’s essentially a slight variation on the prisoners’ dilemma. See for yourself:

You can see another example here, or you can see related videos directly through YouTube. (You now have a little window into the world of how I entertain myself in my free time.) Some questions for you:

  • How is this similar to the prisoners’ dilemma setup? How is it different?
  • Are the players’ choices an equilibrium set of strategies? Why or why not?
  • What would you do if you were playing this game?

I will follow up with some discussion in a couple of days (to give everyone a chance to ponder if they so choose). I will also work on a new tag line having to do with economists liking golden balls. =P

Tags: Game Theory · Videos

10 responses so far ↓

  • 1 JonathanL // Oct 28, 2009 at 2:18 pm

    Nice videos. But a note on the prisoners’ dilemma:

    Just as how in the video, people who know/are friends with Sarah will view her differently… as someone who can be bought, chooses money over friends, etc etc… well, at least I hope so

  • 2 Lucas M. Engelhardt // Oct 28, 2009 at 2:55 pm

    My obsession with British TV extends to Big Brother – where, a season ago, they played a similar game, but with a somewhat different outcome.

    Personally, I think the biggest problem with experiments involving Prisoner’s Dilemmas is that we ignore unobservable sources of utility/disutility. Things like “feeling like I got ripped off” or “looking like a materialistic jerk on national TV” certainly may have an impact on payoffs – and therefore, on strategies and equilibrium.

  • 3 Jason Welker // Oct 29, 2009 at 5:48 am

    Each player has a weakly dominant strategy, which is to choose to steal. By choosing to steal, the player has a chance at maximizing his own payoff, but will do no worse than he would if his opponent also chooses to steal and at least will have the satisfaction of thwarting his opponent’s attempt to steal the money. Looking at it another way, the options were to split and EITHER win 50,000 or nothing, or steal and either win 100,000 or nothing. Clearly the dominant strategy is the latter option.

    There are three Nash equilibria in the game (split/steal, steal/split and steal/steal) which are outcomes at which a player can not unilaterally improve his or her payoff by changing his or her strategy. The outcome Steve was hoping for by chosing “split” (50/50) was not a Nash equilibrium because Sarah knows she can do better if she chooses steal when Steve chooses split. Steve doomed himself by choosing split because he should know that Sarah’s dominant strategy is to choose steal. However, Sarah would also have doomed herself by choosing split because she should assume that Steve would also chose steal since steal is a dominant strategy for him too.

    Steve is shown to be the sucker and Sarah the coldly rational self-interested player. The best chance for Steve to go home with any money would have been for him to use the one minute of discussion time to convince Sarah that he would choose SPLIT, yet be willing to go home with something LESS THAN $50,000 and accept that Sarah was going to choose STEAL. He could have threatened to chose steal if she did not agree to share her winnings with him to some extent. Then again, any promise Sarah makes she could later break, thus further empowering the players to choose steal.

  • 4 Ted // Oct 29, 2009 at 3:07 pm

    Grammar points to you for being the only person on a blog I’ve seen this week to use the plural possessive correctly.

  • 5 econgirl // Oct 29, 2009 at 9:43 pm

    My mother is an English teacher, and, as such, I try to avoid embarrassing her too often.

  • 6 Sean Reitmeyer // Nov 6, 2009 at 9:00 pm

    It is also important that any model reflecting this game show internalizes both the psychological social enforcement of being broadcast as well as the psychic costs of feeling like a sucker into the payout.

    An interesting question – especially as a young single guy (as i am)- in that situation, how much would I be willing to pay for a chance to signal to millions of peoples just how f’ing great of a human being I am.? IE:

    “Listen baby doll, you know I am a reliable, honest, sweet, maybe a bit gullible but with the noblest intentions, type of guy as is evident from my actions on The Golden Balls”

    Considering how much we spend on continuously beefing up our social resume, that might turn out to be one of the less costly signals.

    Of course, there is probably a point where the MC exceed MB as the pot sizes grows.

    On the other point, even though monetarily the payout is 0 both if steal/steal and split/steal for player A, I think the behavioral aversion to feeling like a sucker introduces additional psychic costs to the payout structure. I think this is a deeply motivating bias that doesn’t seem to get enough acknowledgment.

  • 7 Seamus Coffey // Apr 5, 2010 at 2:30 pm

    A short paper using this TV show as a natural experiment of the Prisoner’s Dilemma can be accessed at:

    Economic Incentives – The Goldenballs Dilemma

    The conclusion: Gender, age, occupation and hair colour! matter.

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