Bandwagon effect in mean-field games

This paper provides a mean-field game theoretic model of the bandwagon effect in social networks. The latter phenomenon can be observed whenever individuals tend to align their own opinions to a mainstream opinion. The contribution is three-fold. First, we provide a mean-field games framework that describes the opinion propagation under local interaction. Second, we establish mean-field equilibrium strategies in the case where the mainstream opinion is stationary. Such strategies are shown to have a threshold structure. Third, we study conditions under which a given opinion distribution is stationary if agents implement optimal non-idle and threshold strategies. © 2013 IEEE

Opinion dynamics and stubbornness through mean-field games

This paper provides a mean field game theoretic interpretation of opinion dynamics and stubbornness. The model describes a crowd-seeking homogeneous population of agents, under the influence of one stubborn agent. The game takes on the form of two partial differential equations, the Hamilton-Jacobi-Bellman equation and the Kolmogorov- Fokker-Planck equation for the individual optimal response and the population evolution, respectively. For the game of interest, we establish a mean field equilibrium where all agents reach "-consensus in a neighborhood of the stubborn agent's opinion. ©2013 IEEE

Mean-Field Games and Dynamic Demand Management in Power Grids

This paper applies mean-field game theory to dynamic demand management. For a large population of electrical heating or cooling appliances (called agents), we provide a mean-field game that guarantees desynchronization of the agents thus improving the power network resilience. Second, for the game at hand, we exhibit a mean-field equilibrium, where each agent adopts a bang-bang switching control with threshold placed at a nominal temperature. At equilibrium, through an opportune design of the terminal penalty, the switching control regulates the mean temperature (computed over the population) and the mains frequency around the nominal value. To overcome Zeno phenomena we also adjust the bang-bang control by introducing a thermostat. Third, we show that the equilibrium is stable in the sense that all agents' states, initially at different values, converge to the equilibrium value or remain confined within a given interval for an opportune initial distribution. © 2013 Springer Science+Business Media New York

Game Theoretic Decentralized Feedback Controls in Markov Jump Processes

This paper studies a decentralized routing problem over a network, using the paradigm of mean-field games with large number of players. Building on a state-space extension technique, we turn the problem into an optimal control one for each single player. The main contribution is an explicit expression of the optimal decentralized control which guarantees the convergence both to local and to global equilibrium points. Furthermore, we study the stability of the system also in the presence of a delay which we model using an hysteresis operator. As a result of the hysteresis, we prove existence of multiple equilibrium points and analyze convergence conditions. The stability of the system is illustrated via numerical studies