Chicken Prisoners

By | 2012-04-23

The Prisoner’s Dilemma is a well-known example from game theory. The basic idea is:

Two men are arrested as being involved in the same crime. The police offer both the same deal: testify against your partner and you will go free and your partner goes down for twelve years. If you both remain silent, you will both serve one year. If you both talk you will both get three years.

It’s assumed that neither cares about honour, only about spending the least amount of time in prison as possible. The strange logic of the game ends up telling us that even though they would, in aggregate be best served by cooperating and keeping silent (each serving only one year), they are individually forced to betray their partner. This is because the individual best outcome is that your partner stays silent while you betray. You must assume your partner knows this and reasons identically and will therefore betray you — your only choice then is between three years in prison (if you betray as well) or twelve if you stay silent.

There is a game show on British television called Golden Balls. There are a number of rounds with different rules, but it ends in a round very similar to the prisoner’s dilemma, when only two players remain.

There is a prize pot that has been accumulated over the previous rounds. Each player must choose whether to “split” or “steal”. If both split, they share the pot 50/50. If one splits and one steals, the stealer wins 100% of the pot. If both steal they both win nothing.

It is superficially similar to the prisoner’s dilemma, but with one key difference:

  • In the prisoner’s dilemma, once one party has betrayed, there is an advantage to the second party betraying.
  • In Golden Balls, once one party has betrayed the betrayed party goes away with nothing, regardless of what they choose.

There is a more fundamental difference, not to do with the game rules. In Golden Balls, there is a “negotiation phase”. That negotiation typically takes the form of trying to persuade your partner that you are honest and are going to split. The few times I’ve seen it, it goes one of three ways:

  • Both dishonest, claim they will split, then steal and go with nothing
  • One honest, one dishonest; both claim they will split, one steals the whole amount.
  • Both honest; claim they will split and do. Share the prize.

I’ve seen it enough to realise that, ignoring your own morality, the best course of action is to persuade your partner you are honest, then steal. However, if you don’t ignore morality and are honest, then you don’t want 100%, and your chance at 50% is obtained by splitting. Hence, I would always split.

That was all background. Now watch this clip; the most interesting negotiation phase Golden Balls will ever have.

Watched it? You should, as I’m about to spoil it for you if you haven’t.

I’m disappointed in myself that I never realised that this is the best tactic. You should definitely tell your partner that you are going to steal; this changes the game completely. So much so that if the public weren’t ever realised, Golden Balls would have to be cancelled.

Rightie tells Leftie that he’s definitely going to steal; but (and this is the key part) he will share it with him. The logic is excellent, “I am trustworthy and I know I am trustworthy. Once the money is in my control, I know that I will get 50% of it. I do not know you and don’t know whether you are trustworthy. Therefore I must steal, and you must trust me.” This leaves Leftie with a different choice than is usual in the game — having been convinced that your partner will steal, your choice is between a guaranteed nothing, and a chance at 50%. The play is therefore logically inevitable, you must split and hope your partner is honest.

Rightie then delivers the coup de grace — in fact it doesn’t matter personally to him that he does this (since if he is honest, he will split anyway), but it is a wonderful end — having convinced leftie that he is going to steal (and why would you lie about that?), he chooses split. This is a master stroke not because it changes his own outcome — he either gets 50% if Leftie reasons correctly (and ignores his human desire for malice), or 0% if Leftie cuts off his nose to spit his face. It is a master stroke because it ensures that whatever happens, the banker doesn’t get the money.

What Rightie has done is convert the game from one approximating the Prisoner’s Dilemma to one approximating Chicken for Leftie. “Chicken” is where each player chooses “destroy” or “avoid”. If either chooses destroy, both are destroyed. If either avoids, both walk away, but the one that didn’t avoid is “the winner”. In case you can’t tell, this is the game of Global Thermonuclear War. In Leftie’s case, he has to assume it is a special case of Chicken with Rightie trustworthy. If he chooses “steal”, then it is mutually assured destruction.

Once this strategy is widely known, everyone who plays Golden Balls should implement it. Then it simply becomes a matter of who can get the offer out first.

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