  We consider the general problem of resource sharing in societal networks,
consisting of interconnected communication, transportation, energy and other
networks important to the functioning of society. Participants in such network
need to take decisions daily, both on the quantity of resources to use as well
as the periods of usage. With this in mind, we discuss the problem of
incentivizing users to behave in such a way that society as a whole benefits.
In order to perceive societal level impact, such incentives may take the form
of rewarding users with lottery tickets based on good behavior, and
periodically conducting a lottery to translate these tickets into real rewards.
We will pose the user decision problem as a mean field game (MFG), and the
incentives question as one of trying to select a good mean field equilibrium
(MFE). In such a framework, each agent (a participant in the societal network)
takes a decision based on an assumed distribution of actions of his/her
competitors, and the incentives provided by the social planner. The system is
said to be at MFE if the agent's action is a sample drawn from the assumed
distribution. We will show the existence of such an MFE under different
settings, and also illustrate how to choose an attractive equilibrium using as
an example demand-response in energy networks.
