JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. American Association for the Advancement of Science is collaborating with JSTOR to digitize, preserve and extend access to Science. Axelrod's model of the evolution of cooperation was based on the iterated Prisoner's Dilemma. Empirical work following this approach has helped establish the prevalence of cooperation based on reciprocity. Theoretical work has led to a deeper understanding of the role of other factors in the evolution of cooperation: the number of players, the range of possible choices, variation in the payoff structure, noise, the shadow of the future, population dynamics, and population structure. Although we shall concentrate on theoretical work, it is important to note that scholars have been active in pursuing empirical applications of the theory. Huth (4) found that military conflict during the last century was most successfully deterred when a challenge was met with reciprocity. Cooperation based on reciprocity has been supported for vampire bats (5, 6), vervet monkeys (7), and sessile invertebrates (8). Experimental simulations of defection have been presented to stickleback fish (9) and tree swallows (10); the findings are consistent with reciprocity. On the other hand, Nol (11) rejected reciprocity as an explanation of cooperation between the sexes in chick-rearing by the American oyster catcher, arguing that data on foraging trips and energy use support a theory based on the efficient allocation of energy by the birds. Other investigators have pointed to the difficulties in determining whether observed cooperation is due to a tit-for-tat-like process (12). Despite these difficulties, cooperation based upon reciprocity has received substantial empirical support. In addition, advice has been offered for problems of breach of contracts (13), child custody (14), superpower negotiations (15), and international trade (16, 17). We begin our analysis of recent theoretical work on the evolution of cooperation by reviewing Axelrod's original formulation and theoretical results (2). Is there any reason for an individual to cooperate when noncooperative behavior is rewarded? This question underlies the problem of cooperation in the Prisoner's Dilemma. In the Prisoner's Dilemma, each player has two choices: cooperate or defect (Fig. 1) . The choice may or may not be made rationally. In either case, if the game is only played once, then each player gets a higher payoff from defecting than from cooperating, regardless of what the other player does. However, if both players R.
The traditional iterated Prisoner's Dilemma game has been used widely to study the evolution of cooperation, and a theory of cooperation based on reciprocity is found in many existing literatures such as in REF .
the Further Evolution of Cooperation
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