  In this second part of our work, we study the steady state of the population
and the social utility for the three dynamics SSD, NBRD and NRPM; which were
introduced in the first part. We provide sufficient conditions on the network
based on a maximum payoff density parameter of each node under which there
exists a unique Nash equilibrium. We then utilize positive correlation
properties of the dynamics to reduce the flow graph in order to provide an
upper bound on the steady state social utility. Finally we extend the idea
behind the sufficient condition for the existence of a unique Nash equilibrium
to partition the graph appropriately in order to provide a lower bound on the
steady state social utility. We also illustrate interesting cases as well as
our results using simulations.
