Game dynamics for players with complex personalities

We consider populations of individuals who are engaged in n--person public
good games or in two--person non symmetric or symmetric social dilemma
games. The players imitate the most attractive strategies, and the choice
is motivated not only by their payoffs, but also by their popularity in the
population. The aggregated parameter which determines the influence of
these two factors on the strategy choice of the players is identified with
the sensitivity to reinforcements parameter in the Hernstein's Matching
Law of mathematical psychology. The idea of of imitating the most
successful, and the copying the most popular strategies leads to
stabilization of cooperation in the populations of individuals in the
considered classes of games. The level of cooperation depends on the
sensitivity to reinforcements. We discuss the existence of equilibria and
their stability for such populations. A unique threshold of the
sensitivity is found, below which the polymorphic equilibria are stable,
and above which they are unstable.