3 - Taking the Prisoner's Dilemma seriously: what can we learn from a trivial game?

Summary

The Prisoner's Dilemma in my title refers to a one-shot two-person game with the extensive form shown in Figure 3.1:

In Figure 3.1, player 1 chooses C or D. Player 2 does not know which was chosen. The two different nodes where player 2 chooses are contained within a single information set, represented by the dotted oval. The pairs of numbers at the terminal nodes represent the preferences of respectively player 1 and player 2, with larger numbers indicating outcomes that are higher in their separate preference rankings. Whenever I refer to the Prisoner's Dilemma, it is this game that I am talking about. I have followed convention in labeling the two strategies of the two players “C” and “D,” which suggests that C is a strategy of cooperation and D a strategy of defection. Because the strategy choice of player 1 is contained within a single information set, the game is equivalent to one involving simultaneous play. It makes no difference whether player 1 is depicted as moving first or player 2 is depicted as moving first. The normal or strategic form shown in Figure 3.2 represents the game more compactly.

The payoffs are ordinal utilities – that is, indicators of preference ordering. The first number in each pair indicates the preference ranking of player 1, while the second number indicates the preference ranking of player 2. These numbers only indicate the ranking. They have no other significance. So, for example, if one were to substitute 12 for one of the 4s in either representation of the game, 12,468 for the other, and −36 for both of the 1s, it would make no difference to the game.

As I have argued elsewhere, the preferences that are indicated by the utilities in games are total subjective comparative evaluations. What this means is the following:

1. Preferences are subjective states that combine with beliefs to explain choices. They cannot be defined by behavior, contrary to what revealed preference theorists maintain. Just consider the Prisoner's Dilemma game, which represents player 1 as preferring the outcomes where player 2 chooses strategy C to the outcomes where player 2 chooses strategy D.