Opinion exchange dynamics (Q2362680)

Many of the models of information exchange on networks are intimately related to nice mathematical concepts, often coming from probability, discrete mathematics, optimization and information theory. The survey explains how the theories of Markov chains, martingale arguments, influences and graph limits all play a crucial role in analyzing these models. The authors establish a solid mathematical framework in which common terms like: state of the world, agent and its private signals, social network, convergence, unanimity, agreement and learning, known and frequently used in economical and sociological sciences get their precise meanings. Then, they discuss from the mathematical point of view two main groups of models. The first one, the heuristic models, include the classical DeGroot model, the voter model and the model based on deterministic iterated dynamics. Every model is defined and discussed, and some possible extensions and generalizations are suggested. Similarly, the authors present certain Bayesian models, sequential models among them. As they suggest, some of the arguments and models they present may fit well as classroom materials or exercises in a graduate course in probability. In my opinion this survey can serve as one side of a bridge between mathematicians and people working on problems involving opinion and information exchange and learning.