17 research outputs found
Eminence Grise Coalitions: On the Shaping of Public Opinion
We consider a network of evolving opinions. It includes multiple individuals
with first-order opinion dynamics defined in continuous time and evolving based
on a general exogenously defined time-varying underlying graph. In such a
network, for an arbitrary fixed initial time, a subset of individuals forms an
eminence grise coalition, abbreviated as EGC, if the individuals in that subset
are capable of leading the entire network to agreeing on any desired opinion,
through a cooperative choice of their own initial opinions. In this endeavor,
the coalition members are assumed to have access to full profile of the
underlying graph of the network as well as the initial opinions of all other
individuals. While the complete coalition of individuals always qualifies as an
EGC, we establish the existence of a minimum size EGC for an arbitrary
time-varying network; also, we develop a non-trivial set of upper and lower
bounds on that size. As a result, we show that, even when the underlying graph
does not guarantee convergence to a global or multiple consensus, a generally
restricted coalition of agents can steer public opinion towards a desired
global consensus without affecting any of the predefined graph interactions,
provided they can cooperatively adjust their own initial opinions. Geometric
insights into the structure of EGC's are given. The results are also extended
to the discrete time case where the relation with Decomposition-Separation
Theorem is also made explicit.Comment: 35 page
An integral control formulation of Mean-field game based large scale coordination of loads in smart grids
Pressure on ancillary reserves, i.e.frequency preserving, in power systems
has significantly mounted due to the recent generalized increase of the
fraction of (highly fluctuating) wind and solar energy sources in grid
generation mixes. The energy storage associated with millions of individual
customer electric thermal (heating-cooling) loads is considered as a tool for
smoothing power demand/generation imbalances. The piecewise constant level
tracking problem of their collective energy content is formulated as a linear
quadratic mean field game problem with integral control in the cost
coefficients. The introduction of integral control brings with it a robustness
potential to mismodeling, but also the potential of cost coefficient
unboundedness. A suitable Banach space is introduced to establish the existence
of Nash equilibria for the corresponding infinite population game, and
algorithms are proposed for reliably computing a class of desirable near Nash
equilibria. Numerical simulations illustrate the flexibility and robustness of
the approach
A dynamic game model of collective choice in multi-agent systems
Inspired by successful biological collective decision mechanisms such as honey bees searching for a new colony or the collective navigation of fish schools, we consider a scenario where a large number of agents engaged in a dynamic game have to make a choice among a finite set of different potential target destinations. Each individual both influences and is influenced by the group's decision, as represented by the mean trajectory of all agents. Agents are assumed linear and coupled through a modified form of quadratic cost, whereby the terminal cost captures the discrete choice component of the problem. Following the mean field games methodology, we identify sufficient conditions under which allocations of destination choices over agents lead to self replication of the overall mean trajectory under the best response by the agents. Importantly, we establish that when the number of agents increases sufficiently, (i) the best response strategies to the self replicating mean trajectories qualify as epsilon-Nash equilibria of the population game; (ii) these epsilon-Nash strategies can be computed solely based on the knowledge of the joint probability distribution of the initial conditions, dynamics parameters and destination preferences, now viewed as random variables. Our results are illustrated through numerical simulations
Nash Certainty Equivalence in Large Population Stochastic Dynamic Games: Connections with the Physics of Interacting Particle Systems
We consider large population dynamic games and illuminate methodological connections with the theory of interacting particle systems. Combined with the large population modelling, a Nash Certainty Equivalence (NCE) Methodology is introduced for specifying the localized strategy selection of a given agent within the Nash equilibrium setting. The NCE methodology closely parallels that found in the study of uncontrolled interacting particle systems within the framework of the McKean-Vlasov equation [19]: for both problems the solution is derived by focussing on a single generic individual at a microscopic level and analyzing its interaction with the ensemble of the other individuals of which it is itself, in a statistical sense, a representative