The Prisoner’s Dilemma
The Prisoner’s Dilemma is the best-known game in game theory and a model with wide-ranging applications. It has become a generic phrase for the competition between individual self-interest and group motivation, but the game represents a direct challenge to basic assumptions of classical market economics. Adam Smith taught that through pure competition “the invisible hand” of the marketplace would guide the factors of supply and demand so that goods and services were produced most efficiently at the lowest price. The Prisoner’s Dilemma questions whether that is necessarily the case. Examples of the Prisoner’s Dilemma can be seen in social interaction of all kinds. In this seemingly simple game, players have two choices: to cooperate, or not. In game theory, the term used for choosing to not cooperate is “defect.”
Cooperating involves trust, and this makes the game complex. The Prisoner’s Dilemma was first developed in 1950 at the RAND Corporation. John Nash had made an important discovery related to non-zero-sum games, those games where player’s interests are not in complete opposition. Now known as the Nash equilibrium (Chapter 20), it involves proof of the existence of equilibrium points in every game. These equilibrium points are outcomes where the players have no incentive to change their decision.
Merrill Flood and Melvin Dresher developed a game to see whether people who had no knowledge of equilibrium points would tend to select these outcomes when they played a game. Armen Alchian of UCLA and John D. Williams of RAND played a game with each other repeatedly, using a simple two-by-two matrix where each could choose to cooperate or defect (Table 12.1).
The game is shown in Table 12.1.
This game has only one Nash equilibrium, or supposedly rational outcome where neither player would change his decision. It is the lower left quadrant. In each of the other quadrants either row or column or both could improve his outcome by changing his choice. The lower left is the stable equilibrium that Nash said always exists, which should be the solution to the non-zero-sum, two-person game. It is a simple and obvious solution, because both players have dominant strategies to follow. However, the upper right quadrant has better payoffs for both players and is the best collective outcome. Was the Nash equilibrium the rational solution to the game?