The hipster effect: When anti-conformists all look the same
In such different domains as neurosciences, spin glasses, social science, economics and finance, large ensemble of interacting individuals following (mainstream) or opposing (hipsters) to the majority are ubiquitous. In these systems, interactions generally occur after specific delays associated to transport, transmission or integration of information. We investigate here the impact of anti-conformism combined to delays in the emergent dynamics of large populations of mainstreams and hipsters. To this purpose, we introduce a class of simple statistical systems of interacting agents composed of (i) mainstreams and anti-conformists in the presence of (ii) delays, possibly heterogeneous, in the transmission of information. In this simple model, each agent can be in one of two states, and can change state in continuous time with a rate depending on the state of others in the past. We express the thermodynamic limit of these systems as the number of agents diverge, and investigate the solutions of the limit equation, with a particular focus on synchronized oscillations induced by delayed interactions. We show that when hipsters are too slow in detecting the trends, they will consistently make the same choice, and realizing this too late, they will switch, all together to another state where they remain alike. Similar synchronizations arise when the impact of mainstreams on hipsters choices (and reciprocally) dominate the impact of other hipsters choices, and we show that these may emerge only when the randomness in the hipsters decisions is sufficiently large. Beyond the choice of the best suit to wear this winter, this study may have important implications in understanding synchronization of nerve cells, investment strategies in finance, or emergent dynamics in social science, domains in which delays of communication and the geometry of information accessibility are prominent.