The dynamics of indirect reciprocity

Richard Alexander has argued that moral systems derive from indirect reciprocity. We analyse a simple case of a model of indirect reciprocity based on image scoring. Discriminators provide help to those individuals who have provided help. Even if the help is never returned by the beneficiary, or by individuals who in turn have been helped by the beneficiary, discriminating altruism can be resistant against invasion by defectors. Indiscriminate altruists can invade by random drift, however, setting up a complex dynamical system. In certain situations, defectors can invade only if their invasion attempts are sufficiently rare. We also consider a model with incomplete information and obtain conditions for the stability of altruism which differ from Hamilton's rule by simply replacing relatedness with acquaintanceship.