by R S

qu th t at em cie oun op their behaviour on the outcome of previous interactions (Axelro Sigmun of coop becaus behavio city, h recogn main-e use those mund ists of lations neral-their partners and base their decision solely on the Proc. R. Soc. B (2005) 272, 1115–1120*Author for correspondence (thomas.pfeiffer@inf.ethz.ch).their previous encounter, or if individuals interactwith only one partner for a long time (Dugatkin 2002). Thus, direct reciprocity either requires specific cognitive capabilities of the interacting individuals (Milinski & Wedekind 1998) or requires a very specific population structure such that the latter mechanism can take effect. Behavioural studies on humans (Berkowitz & Daniels 1964) and a novel behavioural study on rats (Rutte & ized reciprocity in larger groups. We assume that individuals interact repeatedly within their group. In each round, two individuals of a group are chosen randomly to interact in a ‘one-shot ’ PD. After a sufficiently large number of interactions such that the average payoffs can be approximated by the payoffs for an infinite number of interactions (Nowak & Sigmund 1993, 1994), the groups are dissolved and new groups are formed randomly from the population. Furthermore, we assume that individuals do not recognizeReceived Acceptedh cooperation in a population of selfish individuals d & Hamilton 1981; Axelrod 1984; Nowak & d 1992, 1993). This mechanism for the evolution eration is often referred to as ‘direct reciprocity’ e individuals can reciprocate previous cooperative ur of their partners ( Trivers 1971). Direct recipro-owever, can only be successful if individuals ize their partner and remember the outcome of OF GENERALIZED RECIPROCITY To study whether cooperation can evolve and be tained in a population by generalized reciprocity, w population dynamical simulations, analogous to used for studying direct reciprocity (Nowak & Sig 1993, 1994). We assume that the population cons groups of n individuals. Here, we first describe simu for groups of three individuals and then discuss gewith the present partner, such as tit-for-tat ( TFT), may establi