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Mathematical Models of Social Evolution: A Guide for the Perplexed$
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Richard McElreath and Robert Boyd

Print publication date: 2007

Print ISBN-13: 9780226558264

Published to Chicago Scholarship Online: February 2013

DOI: 10.7208/chicago/9780226558288.001.0001

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(p.123) Chapter 4 Reciprocity
Mathematical Models of Social Evolution: A Guide for the Perplexed

Richard Mcelreath

Robert Boyd

University of Chicago Press

In most primate societies, individuals have long-lasting relationships with other members of their groups. Individual monkeys often have preferred grooming partners and reliable allies. If allies and grooming partners were always relatives, we could explain such cooperation with inclusive fitness and move on. But these cooperative relationships involve unrelated individuals. How can natural selection lead to such behavior in the absence of kinship? One answer is reciprocity: I'll scratch your back if you scratch mine. The essential feature of reciprocity is contingent cooperation. The concept of reciprocity took off in 1981 when Robert Axelrod and W. D. Hamilton published a paper in Science that analyzed a formal model of reciprocal altruism. This chapter examines both the basic Axelrod-Hamilton model of reciprocity and some of the more important developments since, including the importance of mistakes, the effect of partner choice, indirect reciprocity, kinship, mutants, Tit-for-Tat strategy, and the roles of reciprocity and altruistic punishment in solving collective action problems. The chapter also explains how to build and solve models of repeated interactions.

Keywords:   Axelrod-Hamilton model, mutants, mistakes, partner choice, indirect reciprocity, reciprocity, collective action, Tit-for-Tat strategy, altruistic punishment, kinship

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