  Given that the assumption of perfect rationality is rarely met in the real
world, we explore a graded notion of rationality in socioecological systems of
networked actors. We parametrize an actors' rationality via their place in a
social network and quantify system rationality via the average Jensen-Shannon
divergence between the games Nash and logit quantal response equilibria.
Previous work has argued that scale-free topologies maximize a system's overall
rationality in this setup. Here we show that while, for certain games, it is
true that increasing degree heterogeneity of complex networks enhances
rationality, rationality-optimal configurations are not scale-free. For the
Prisoner's Dilemma and Stag Hunt games, we provide analytic arguments
complemented by numerical optimization experiments to demonstrate that
core-periphery networks composed of a few dominant hub nodes surrounded by a
periphery of very low degree nodes give strikingly smaller overall deviations
from rationality than scale-free networks. Similarly, for the Battle of the
Sexes and the Matching Pennies games, we find that the optimal network
structure is also a core-periphery graph but with a smaller difference in the
average degrees of the core and the periphery. These results provide insight on
the interplay between the topological structure of socioecological systems and
their collective cognitive behavior, with potential applications to
understanding wealth inequality and the structural features of the network of
global corporate control.
