Prisoner's dilemma & chicken

I recently finished reading William Poundstone's book, Prisoner's Dilemma: John von Neumann, Game Theory, and the Puzzle of the Bomb, so I've got game theory on my mind, and that's what today's post is about. My apologies to reader Jill, who'll stop reading about…now.

Prisoner's dilemma

For years I've called any social dilemma where there exists a conflict between the good of the group and the good of the individual a prisoner's dilemma, but this is wrong. In the language of game theory, a prisoner's dilemma is a specific kind of social dilemma, and the other social dilemmas have their own names.

What all social dilemmas have in common is two or more people deciding, independently of others, whether to cooperate or to defect. In each dilemma, defection brings about a reward for the defector and punishment for the cooperator, though mutual defection is an undesired outcome. Prisoner's dilemma is the best known of the dilemmas because it's the most brutal: defecting is always the better choice for the individual despite mutual defection being undesirable. As a decision table, it looks like this.

	Cooperate	Defect
Cooperate	3, 3	1, 4
Defect	4, 1	2, 2

The way to read the table goes as follows: in each cell, the first number represents the payoff for the player whose choice determines which row to use, and the second number represents the payoff for the player whose choice determines the column. Each payoff is ranked from 1 to 4, with higher numbers being better for that person. For example, if the row player (Player 1) defects, and the column player (Player 2) cooperates, then we follow the defect row and the cooperate column and see that Player 1 is rewarded with a 4 (top score) and Player 2 is punished with a 1 (lowest score).

As you can see from the table, a prisoner's dilemma player is always better off defecting than cooperating even though mutual cooperation beats mutual defection. To see this, imagine you're Player 1, so you must select a row. Player 2 has already made their choice, though you don't know what that choice is. Should Player 2 have decided to defect, then you ought to select the best cell for you in the second column. Your choices are to cooperate and score a 1 or to defect and score a 2, so you're better off defecting. Whereas, should Player 2 have decided to cooperate then you should select the best cell in the first column. Your choices then would be to cooperate and score a 3 or to defect and score a 4, so again you would be better off defecting. The dilemma here is that Player 2 will likely arrive at the same conclusion and thus defect, too. Therefore, in a prisoner's dilemma two rational players will both defect, bringing about a score of 2 for both players. Whereas, two irrational players might have both cooperated and each scored a 3.

That's prisoner's dilemma. What are the other dilemmas?

Chicken

Another dilemma is called chicken. Here's its decision table.

	Cooperate	Defect
Cooperate	3, 3	2, 4
Defect	4, 2	1, 1

Chicken gets its name from any number of popular uses, one being a game where two people each drive a car straight at the other to see who swerves out of the way first. The winner is the macho player who doesn't swerve (score 4) and the loser is the coward who does swerve (score 2), though the catastrophic event here is if both players win, in which case both macho drivers are dead on impact (score 1).

Chicken is a useful scenario for describing a situation whereby everyone involved needs someone to commit to a sacrificial action, but everyone has incentive not to be that person. One example is stopping a well armed and suicidal hijacker; someone needs to stop the hijacker for the good of the group, but individually the best course of action is for someone else to be the hero. In some ways this is worse than the prisoner's dilemma because with prisoner's dilemma there's a fixed rational choice—always defect—but in chicken there's no fixed rational choice: sometimes a player is better off defecting and sometimes they're better off cooperating. Indeed, in a version of chicken where your behavior can affect the other player's decision (though this is not allowed in the strict game-theory version of the game, where both players must make their decision independently of the other), one rational course of action is to convince the other player of your own irrationality, thereby making the other player more fearful of the looming catastrophe of mutual defection and thus more likely to cooperate. But of course the other player can try the same trick on you! Just as with prisoner's dilemma, chicken is a dilemma with no clear, ideal solution.

Next post, I'll describe two more social dilemmas from the book.