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In this second part of our work, we study the steady state of the populationand the social utility for the three dynamics SSD, NBRD and NRPM; which wereintroduced in the first part. We provide sufficient conditions on the networkbased on a maximum payoff density parameter of each node under which thereexists a unique Nash equilibrium. We then utilize positive correlationproperties of the dynamics to reduce the flow graph in order to provide anupper bound on the steady state social utility. Finally we extend the ideabehind the sufficient condition for the existence of a unique Nash equilibriumto partition the graph appropriately in order to provide a lower bound on thesteady state social utility. We also illustrate interesting cases as well asour results using simulations.

Dynamics of a Stratified Population of Optimum Seeking Agents on a Network -- Part II: Steady State Analysis