The  evolution of cooperation among humans has been extensively studied in the last decades (see e.g. the famous work by Axelrod (1984)). However, especially with regard to large-scale societies where interaction is decentralized and involves genetically unrelated individuals, a crucial question remains largely open: how can cooperation endogenously (i) emerge and (ii) be successfully sustained over time? As several scholars persuasively argue, invoking explanations in terms of more or less sophisticated forms of ‘enlightened self-interest’, by referring to interactions occurring among kin (Hamilton 1964), repeated encounters (Fudenberg and Maskin 1986) and reputation formation is definitely not sufficient for accounting for the evidence available about the relevance of cooperation within several significant human contexts where collective action problems naturally arise. In experiments, different player ‘types’ seem to emerge: (1) some subjects are standard selfish maximizers, confirming that the homo oeconomicus exists; (2) other subjects act unselfishly, as if they were driven by other-regarding preferences; (3) a third group of players are willing to nonstrategically punish and/or reward others (i.e. they are driven by some form of ‘strong reciprocity’, often on the basis of an evaluation of the opponent’s intentions). Hence, we ask the following question: can cooperation endogenously emerge and be sustainable over time within a large-scale heterogeneous population composed of three ‘experimentally focal’ types such as egoists, altruists and strongly reciprocal players? This paper provides a theory of why some forms of intention-based strong reciprocity can persist even when evolutionary pressure selects against behaviors yielding lower material payoffs. It is shown that, paradoxically, punishing – rather than rewarding – altruists is successful in enforcing cooperation, whereas other forms of strong reciprocity (such as a simultaneous recourse to the ‘stick’ against egoists and the ‘carrot’ in favor of altruists) turn out to be extremely maladaptive, within a social environment where neither group selection nor assortative interactions are allowed and agents randomly interact over time.

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