  In this work, we aim to contribute to the understanding of the human
pro-social behavior by studying the influence that a particular form of social
pressure "being watched" has on the evolution of cooperative behavior. We study
how cooperation emerge in multiplex complex topologies by analyzing a
particular bidirectionally-coupled dynamics on top of a two-layers multiplex
network (duplex). The coupled dynamics appears between the Prisoner's Dilemma
game in a network, and a threshold cascade model in the other. The threshold
model is intended to abstract the behavior of a network of vigilant nodes, that
impose pressure of being observed altering hence the temptation to defect of
the dilemma. Cooperation or defection in the game also affects the state of a
node of being vigilant. We analyze these processes on different duplex networks
structures and assess the influence of the topology, average degree and
correlated multiplexity, on the outcome of cooperation. Interestingly, we find
that the social pressure of vigilance may impact cooperation positively or
negatively, depending on the duplex structure, specifically the degree
correlations between layers is determinant. Our results give further
quantitative insights in the promotion of cooperation under social pressure.
