  This work is concerned with the dynamics of online cultural markets, namely,
attention allocation of many users on a set of digital goods with infinite
supply. Such dynamic is important in shaping processes and outcomes in society,
from trending items in entertainment, collective knowledge creation, to
election outcomes. The outcomes of online cultural markets are susceptible to
intricate social influence dynamics, particularly so when the community
comprises consumers with heterogeneous interests. This has made formal analysis
of these markets improbable. In this paper, we remedy this by establishing
robust connections between influence dynamics and optimization processes, in
trial-offer markets where the consumer preferences are modelled by multinomial
logit. Among other results, we show that the proportional-response-esque
influence dynamic is equivalent to stochastic mirror descent on a convex
objective function, thus leading to a stable and predictable outcome. When all
consumers are homogeneous, the objective function has a natural interpretation
as a weighted sum of efficiency and diversity of the culture market. In
simulations driven by real-world preferences collected from a large-scale
recommender system, we observe that ranking strategies aligned with the
underlying heterogeneous preferences are more stable, and achieves higher
efficiency and diversity. In simulations driven by real-world preferences
collected from a large-scale recommender system, we observe that ranking
strategies aligned with the underlying heterogeneous preferences are more
stable, and achieves higher efficiency and diversity.
