J. theorl Biol. (1988) 132, 337-356 The Evolution of Reciprocity in Sizable Groups ROBERT BOYD Department of Anthropology, University of California, Los Angeles, CA 90024, U.S.A. AND PETER J. RICHERSON Institute of Ecology, University of California, Davis, CA 95616, U.S.A. (Received 11 August 1987, and in revised form 8 February 1988) Recently, several authors have investigated the evolution of reciprocal altruism using the repeated prisoner's dilemma game. These models suggest that natural selection is likely to favor behavioral strategies leading to reciprocal cooperation when pairs of individuals interact repeatedly in potentially cooperative situations. Using the repeated n-person prisoner's dilemma game, we consider whether reciprocal altruism is also likely to evolve when social interactions involve more individuals. We show that the conditions that allow the evolution of reciprocal cooperation become extremely restrictive as group size increases. Several lines of evidence suggest that sizable groups of people sometimes behave cooperatively, even in the absence of external sanctions against noncooperative behavior. For example, in many food foraging groups, game is shared among all members of the group regardless of who makes the kill (e.g., Kaplan & Hill, 1984; Lee, 1979; Damas, 1971). In many other stateless societies, men risk their lives in warfare with other groups (e.g., Meggit, 1977). There is also evidence that a great deal of cooperation takes place in contemporary state level societies without external sanctions. For example, people contribute to charity, give blood, and vote--even though the effect of their own contributions on the welfare of the group is negligible. The groups benefiting are often very large and composed of very distantly related individuals. Perhaps the most dramatic example of cooperation in contemporary societies are underground movements such as Poland's Solidarity in which people cooperate to achieve a common goal in opposition to all of the power of the modern state (see Olson, 1971, 1982 and Hardin, 1982 for further examples.) Because of the anecdotal nature of these data, it is possible to doubt any particular example. However, psychologists and sociologists have also shown that people cooperate under carefully controlled laboratory conditions, albeit for smaller stakes. For example, Marwell & Ames (1979, 1980) presented individual students with two alternative investments: a low return private investment in which profits accrued to the individual, and a higher return investment in which returns accrued to all group members whether they invested or not. Students invested in the group beneficial investment at a much higher rate than is consistent with rational self interest. (See Dawes, 1980, for a review of such experiments.) 537 0022-5193/88/110337+20 $03.00/0 © 1988 Academic Press Limited