In evolutionary biology, the two major approaches to the emergence of cooperation are kin-selection, on one hand, and reciprocation, on the other. The latter, which is essential for understanding cooperation between non-related individuals and very prominent in human societies, can be subdivided into two parts of unequal size. In direct reciprocity, it is the recipient of a helpful action who eventually returns the aid. In indirect reciprocity, the return is provided by a third party. This possibility has originally been named 'third-party altruism' or 'generalised reciprocity' by Trivers (1971). Later, Alexander (1987) explored it under the (now common) heading of 'indirect reciprocity', see also Ferriere (1998) and Wedekind (1998). Indirect reciprocity is much less well studied than direct reciprocity, and offers interesting theoretical challenges.

Several mechanisms for indirect reciprocity are conceivable. It could be, for instance, that a person having been helped is enclined to help a third party in turn. In cyclical networks, this provides a plausible feedback loop. But studies by Boyd and Richerson (1989) and van der Heijden (1996) suggest that such networks have to be rather small and rigid.

Alexander suggested, in contrast, that indirect reciprocation is based on reputation and status. By giving help to others, individuals acquire a high reputation. If help is directed preferentially towards recipients with a high reputation, defectors will be penalised. Such indirect reciprocation based on reputation and status is the topic of this paper.

The two main reasons why reputation mechanisms are interesting show up at two stages in human evolution which could not be further apart. On the one hand, status and reputation may well have played a major role in the evolution of moral systems since the dawn of prehistory, boosting cooperation between non-relatives (a major cause for the evolutionary success of hominids) and possibly providing a major selective impetus for the emergence of language, as a means of transmitting information about group members through gossip (Alexander, 1987, Nowak and Sigmund, 1998a, Panchanathan and Boyd, 2003). On the other hand, the very recent advent of e-commerce makes the efficient assessment of reputations and moral hazard in trust-based transactions a burning issue. Anonymous one-shot interactions in global markets, rather than long-lasting repeated interactions through direct reciprocation, seem to play an ever-increasing role in today's economy (Bolton et al, 2002, Keser, 2002, Dellarocas, 2003).

The aim of this paper is to provide a survey of the model-based theoretical investigations of the concept of indirect reciprocation, and of the remarkable results on experimental economic games inspired by them.

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