  Experimental studies have shown the ubiquity of altruistic behavior in human
societies. The social structure is a fundamental ingredient to understand the
degree of altruism displayed by the members of a society, in contrast to
individual-based features, like for example age or gender, which have been
shown not to be relevant to determine the level of altruistic behavior. We
explore an evolutionary model aiming to delve how altruistic behavior is
affected by social structure. We investigate the dynamics of interacting
individuals playing the Ultimatum Game with their neighbors given by a social
network of interaction. We show that a population self-organizes in a critical
state where the degree of altruism depends on the topology characterizing the
social structure. In general, individuals offering large shares but in turn
accepting large shares, are removed from the population. In heterogeneous
social networks, individuals offering intermediate shares are strongly selected
in contrast to random homogeneous networks where a broad range of offers, below
a critical one, is similarly present in the population.
