Problems and Pseudo-Problems in Understanding Cooperation in Social Dilemmas

The principal aim of this article is to clarify what is and what is not problematic in understanding cooperation in the dyadic Prisoner’s Dilemma game and in multiplayer social dilemmas. A secondary aim is to provide a brief overview of the most important proposals for solving the genuine problems. Our commentary on the very interesting target article (Krueger, DiDonato, & Freestone, this issue) is embedded in a more general critical review of explanations for cooperation in social dilemmas. We hope to clarify some of the issues that are commonly misunderstood in the wideranging literature on cooperation in social dilemmas. Figure 1 shows the payoff matrix of the Prisoner’s Dilemma game in one of its most familiar forms (e.g., Axelrod, 1984). In the generalized payoff matrix for symmetric 2 × 2 games on the right, any game is a Prisoner’s Dilemma game if the rank order of the payoffs obeys the inequalities T > R > P > S. To play the game, Player I chooses a strategy represented by a row, either C (cooperate) or D (defect), and independently (without knowledge of Player I’s choice) Player II chooses a strategy represented by a column, either C or D. The outcome of the game is one of the four cells where the strategy choices intersect, and the pair of numbers in that cell are the payoffs to the two players, Player I receiving the first payoff and Player II the second. For convenience, payoffs are frequently interpreted as small amounts of money, and for most purposes this is harmless enough, but in formal game theory payoffs are actually utilities representing the players’ preferences among the possible outcomes, taking all relevant factors into account, not only the monetary or other objective values of the payoffs but also feelings of generosity or spite, considerations of fairness, and all other extraneous factors that might affect a player’s preferences. This apparently simple game has attracted more attention from psychologists, economists, political scientists, sociologists, and philosophers than any other, for two main reasons. First, the game provides a simple model of a form of cooperation that arises commonly in social, economic, and political life. To give just one example, consider two restaurants competing for business in a small village and currently achieving equal market shares. Each restaurant manager is deciding whether to introduce a buy-one-get-one-free special offer. If either manager introduces the special offer unilaterally, then it will attract most of the customers from the rival restaurant, and increased revenues will more than offset the costs of the special offer, hence profits will increase; but if both managers introduce the special offer, then each will merely bear the costs without any revenue gains, and hence each will suffer reduced profits. It should be obvious that this is a Prisoner’s Dilemma game in which introducing the special offer corresponds to choosing the defecting D strategy. Any dyadic interaction is a Prisoner’s Dilemma game provided that both agents are better off if they both act in one way (cooperate) rather than another (defect), but each is tempted to defect unilaterally, because that yields the best payoff of all (and the worst of all to the other agent). Situations with this strategic structure are ubiquitous in everyday life. The second reason why the Prisoner’s Dilemma game has attracted so much attention is that it embodies a genuine paradox. Two perfectly rational players, who according to the standard assumptions of game theory know everything that can be known about the game, including the fact that both players are perfectly rational in the sense of always striving to maximize their individual payoffs relative to their knowledge and beliefs at the time of acting, will defect, although they would have received higher individual payoffs if they had both cooperated, and they know that too. The reason why they will defect is that defection yields a better payoff than cooperation whatever the co-player does: In the example in Figure 1 (left), a player receives 5 rather than 3 from defecting rather than cooperating if the co-player cooperates, and 1 rather than 0 from defecting rather than cooperating if the co-player defects. Hence, defection pays better than cooperation irrespective of the co-player’s choice. The technical term for this is strategic dominance: D is a dominant strategy, and there should really be no argument about whether or not it is rational to defect, because it must always be rational to choose a dominant strategy and irrational to choose a dominated strategy. The strategic dominance argument is a straightforward and uncontroversial application to game theory of the sure-thing principle that Savage (1954/1972) included as one of the seven postulates of his axiomatic theory of rational decision making. Strategic dominance solves