Modeling of opinion dynamics and social networks using mean-field games
Due to their wide variety of applications, multi-agent systems are ubiquitous and have, as a consequence, gained interest in recent years.
Such systems arise in a wide range of contexts including robotics, power systems and finance markets. Consequently, different approaches for control design for multi-agent systems are available in the literature. Several of these approaches exploit notions borrowed from game theory.
For game theoretic problems with a large, possibly infinite number of players, the framework provided by mean-field games may be of interest. This is a framework based on stochastic differential equations and dynamic optimization, which allows to model agents aiming at maximizing their own reward while simultaneosuly contributing to the benefit of the whole population.
In this regard, they seem to be particularly well suited to be used for analysis and prediction of opinion dynamics and social networks, where the behaviour of agents, or players, is both driven by the individual interest and influenced by the surrounding community. The problem become particularly interesting when several distinct population of agents are supposed to interact, possibly with adversarial objectives.