On bubbling dynamics generated by a stochastic model of herd behavior

Abstract

This paper suggests a class of stochastic collective learning processes exhibiting very irregular behavior. In particular, there are multimodal long run distributions. Some of these modes may vanish as the population size increases. This may bethought of as bubbles" persistent for a nite range of population sizes but disappearing in the limit. The limit distribution proves to bea discontinuous function of parameters determining the learning process. This gives rise to another type of bubbles": limit outcomes corresponding to small perturbations of parameters are di erent.Since an agent's decision rule involves imitation of the majority c hoice in a random sample of other members of the population, the resulting collective dynamics exhibit herding" or epidemic" features. JEL Classi cation: C72, C73, D83.

Opinion influence and evolution in social networks: A Markovian agents model

“…Rather interestingly, the herding phenomenon was observed in previous studies on social learning, by using quite different models and assumptions, see e.g. [8], [17].…”

“…By standard combinatorial calculus, it follows that Pr{n 1 (t) = k} = ρ k (t) N k . So: Then, recalling (21), (17) and taking the limit for dt tending to zero, the first row of eq. ( 16) is demonstrated.…”

The Impact of Interaction and Social Learning on Aggregate Expectations

“…For example Lux (1998) uses non-linear dynamics to determine supply and demand and then closes the model through an exogenous market maker. A second approach is through a Markov switching process such as Kijima and Uchida (2005) or Gaio et al (2002). A third approach introduces the concept of the social network whereby agents only communicate with, and see the actions and sometimes payoffs of, those agents which they have a connection with.…”