Equilibria in populations of agents with complex personality profiles for 2-player games

We propose a theory of evolution of social systems which generalizes the standard proportional fitness rule of the evolutionary game theory, and a formalism of social interactions in which the actors' choice behavior is controlled by parameters which describe their ability to control the relation between a sequence of stimulus and a sequence of responses. The formalism is applied to describe the dynamics of two-person one-shot games played in infinite populations. In particular it predicts the non-zero level of cooperation in the long run for the Prisoner's Dilemma games.