This past weekend, an entertaining video clip was making the rounds on twitter and in the blogosphere. It is from a British daytime television show called “Golden Balls” and the academic discussion about it has been framed around 2 by 2 game theory:
At the end of the show the contestants have to make one last decision over the final jackpot. They are each presented with two golden balls. One has “split” printed inside it and the other has “steal” printed inside it:
- If both contestants choose the split ball, the jackpot is split equally between them.
- If one contestant chooses the split ball and the other chooses the steal ball, the stealer gets all the money and the splitter leaves empty-handed.
- If both contestants choose the steal ball, they both leave empty-handed.
It is similar to the prisoner’s dilemma in game theory, however, in this game the players are allowed to communicate.
Indeed, the communication is the interesting element of this particular play of the game:
In this game, steal is likely the dominant strategy. If you are certain your opponent is going to split, then it is superior to steal in a single play. You win. If you are certain your opponent is going to steal, then you are indifferent between stealing and splitting, though many people would likely steal just to avoid being made to be the sucker (thinking of relative gains).
Indeed, if we ignore cash values and make the sucker result the 4th-ranked payoff given the logic I’ve just provided about relative gains, then this game would then be a single-shot prisoner’s dilemma game. The dominant strategy is steal (defect). Obviously, preferences over outcomes should determine the strategy one employs in a game. Generally, however, simple game theory assumes utility maximization and the outcomes here are technically the same.
In any case, in this video from “Golden Balls,” player 1 (the man on the right in the brown shirt) has attempted to turn this situation into a different game — chicken, I think — by trying to add a perceived payoff that is worse than playing the sucker in a prisoner’s dilemma.
In chicken, the common story is two teenage drivers head directly for one another at high speed. If they both swerve (yield), this is the mutual split result. If only one swerves, s/he is the chicken and the other player wins. If both continue driving towards one another, they have a horrible accident.
Here, if player 2 selects steal with the knowledge that player 1 is definitely going to steal, then the total prize possible will be ZERO. However, if player 2 lets himself be exploited, then player 1 has dangled the (unenforceable?) promise of sharing the winnings after the show. Effectively, player 1 has attempted to transform the situation by creating the image of a shared victory even when the other player yields. It would be kind of like a fixed boxing match. The payoff comes after the participant takes the dive.
Generally, if one earns a reputation for selecting steal (never swerving) in the game of chicken, then no others will want to play this game with you because their best option is to split (swerve/yield). Why select the outcome that will assuredly result in a disastrous outcome? Unfortunately, one cannot earn a reputation for unyielding play in the first confrontation with an unknown player.
However, in his Introduction to Herman Kahn’s On Escalation, Thomas Schelling recommended that a chicken player should throw the steering wheel out the car window to signal a firm commitment to the steal (not swerve) strategy. Such a player has signaled to the opponent that the result is out of his hands. The best that can be hoped is to avoid disaster.
In this case, to influence Player 2’s choice, Player 1 has essentially communicated that he is tossing the steering wheel out the window.
And then, Player 1 swerves anyway!