Complexity_ A Guided Tour - Melanie Mitchell [102]
Now suppose Russia does not build the weapon in question. Then if you had decided to build it, the United States would have a military edge over Russia, though at some cost to the nation, and if you had decided not to build, the United States and Russia would remain equal in weaponry.
Just as we saw for Bob and Alice, regardless of what Russia is going to do, the rational thing is for you to approve the proposal, since in each case building the weapon turns out to be the better choice for the United States. Of course the Russians are thinking along similar lines, so both nations end up building the new bomb, producing a worse outcome for both than if neither had built it.
This is the paradox of the Prisoner’s Dilemma—in the words of political scientist Robert Axelrod, “The pursuit of self-interest by each leads to a poor outcome for all.” This paradox also applies to the all too familiar case of a group of individuals who, by selfishly pursuing their own interests, collectively bring harm to all members of the group (global warming is a quintessential example). The economist Garrett Hardin has famously called such scenarios “the tragedy of the commons.”
The Prisoner’s Dilemma and variants of it have long been studied as idea models that embody the essence of the cooperation problem, and results from those studies have influenced how scholars, businesspeople, and governments think about real-world policies ranging from weapons control and responses to terrorism to corporate management and regulation.
The Dilemma is typically formulated in terms of a two-person “game” defined by what mathematical game theorists call a payoff matrix—an array of all possible outcomes for two players. One possible payoff matrix for the Prisoner’s Dilemma is given in figure 14.3. Here, the goal is to get as many points (as opposed to as few years in prison) as possible. A turn consists of each player independently making a “cooperate or defect” decision. That is, on each turn, players A and B independently, without communicating, decide whether to cooperate with the other player (e.g., refuse to testify; decide not to build the bomb) or to defect from the other player (e.g., testify; build the bomb). If both players cooperate, each receives 3 points. If player A cooperates and player B defects, then player A receives zero points and player B gets 5 points, and vice versa if the situation is reversed. If both players defect, each receives 1 point. As I described above, if the game lasts for only one turn, the rational choice for both is to defect. However, if the game is repeated, that is, if the two players play several turns in a row, both players’ always defecting will lead to a much lower total payoff than the players would receive if they learned to cooperate. How can reciprocal cooperation be induced?
FIGURE 14.3. A payoff matrix for the Prisoner’s Dilemma game.
Robert Axelrod, of the University of Michigan, is a political scientist who has extensively studied and written about the Prisoner’s Dilemma. His work on the Dilemma has been highly influential in many different disciplines, and has earned him several prestigious research prizes, including a MacArthur foundation “genius” award.
Axelrod began studying the Dilemma during the Cold War as a result of his own concern over escalating arms races. His question was, “Under what conditions will cooperation emerge in a world of egoists without central authority?” Axelrod noted that the most famous historical answer to this question was given by the seventeenth-century philosopher Thomas Hobbes, who concluded that cooperation could develop only under the aegis of a central authority. Three hundred years (and countless wars) later, Albert Einstein similarly proposed