Social benefits of criticality-induced psychological reward

Abstract

This article deals with the issue of evolutionary game theory by adopting the key ingredient of criticality borrowed from the field of phase transitions to establish the social benefit of altruism. The theoretical perspective that we propose rests on the dynamics of a Nash system modulated by the behavioral dynamics of the units of this system. The players of the network under study are naturally led to make the selfishness choice, but due to the imitation principle they may also make the altruism choice if some of their neighbors are altruist. We prove that if the imitation strength K is assigned a special value Kc a phase transition occurs to the emergence of altruism. This form of phase transition is similar to the phase transition processes of physics but it is significantly extended, due to the fact that the sociological system does not fit the thermodynamic limit condition. As a consequence at criticality the concentration of altruists is characterized by large fluctuations that have the effects of significantly enhancing the financial benefits generated by the psychological reward for altruism recently introduced by Gintis for a modified version of Nash game theory. We argue that the feedback of the financial level on the behavioral level will lead to a plausible explanation of the emergence of altruism in human societies.