Opinion Dynamics and Stubbornness Via Multi-Population Mean-Field Games

Abstract

This paper studies opinion dynamics for a set of heterogeneous populations of individuals pursuing two conflicting goals: to seek consensus and to be coherent with their initial opinions. The multi-population game under investigation is characterized by (i) rational agents who behave strategically, teractions. The main contribution of this paper is to encompass all of these aspects under the unified framework of mean-field game theory.We show that, assuming initial Gaussian density functions and affine control policies, the Fokker-Planck-Kolmogorov equation preserves Gaussianity over time. This fact is then used to explicitly derive expressions for the optimal control strategies when the players are myopic. We then explore consensus formation depending on the stubbornness of the involved populations: we identify conditions that lead to some elementary patterns, such as consensus, polarization or plurality of opinions.Finally, under the baseline example of the presence of a stubborn population and a most gregarious one, we study the behavior of the model with a finite number of players, describing the dynamics of the average opinion, which is now a stochastic process. We also provide numerical simulations to show how the parameters impact the equilibrium formation.

Opinion Dynamics with Bayesian Learning

“…All the opinion update strategies can be classified into two categories by using Bayesian update rule or not: one is Bayesian update strategy and the other is non-Bayesian strategy. Non-Bayesian learning refers to individuals updating their opinions by non-Bayesian strategy, such as linear combination of opinions of the neighbors [5,15,16] and various game theories in social network [17,18]. Most of these models try to explore how the society could achieve group consensus.…”

Learning Deep Mean Field Games for Modeling Large Population Behavior

“…In the other direction, RL enables us to devise a data-driven method for solving an MFG model of a real-world system for temporal prediction. While research on the theory of MFG has progressed rapidly in recent years, with some examples of numerical simulation of synthetic toy problems, there is a conspicuous absence of scalable methods for empirical validation (Lachapelle et al, 2010;Achdou et al, 2012;Bauso et al, 2016). Therefore, while we show how MFG is well-suited for the specific problem of modeling population behavior, we also demonstrate a general data-driven approach to MFG inference via a synthesis of MFG and MDP.…”

“…In this limit, an agent population is represented via their distribution over a state space, and each agent's optimal strategy is informed by a reward that is a function of the population distribution and their aggregate actions. The stochastic differential equations that characterize MFG can be specialized to many settings: optimal production rate of exhaustible resources such as oil among many producers (Guéant et al, 2011); optimizing between conformity to popular opinion and consistency with one's initial position in opinion networks (Bauso et al, 2016); and the transition between competing technologies with economy of scale (Lachapelle et al, 2010). Representing agents as a distribution means that MFG is scalable to arbitrary population sizes, enabling it to simulate real-world phenomenon such as the Mexican wave in stadiums (Guéant et al, 2011).…”

Climb on the Bandwagon: Consensus and Periodicity in a Lifetime Utility Model with Strategic Interactions

“…Two remarks are needed. Firstly, the lifetime setup immediately refers to a parallel strand of literature, related to more classical optimization problems for consensus formation (see [20], [31], [3]). The second remark pertains to the modeling structure of the society; in order to study into details (and possibly to obtain closed-form solutions) the relationship between social interaction and frictions in changing opinion, we stick with the simplest possible geometry: a mean-field model.…”