  This paper develops a clustering method that takes advantage of the
sturdiness of model-based clustering, while attempting to mitigate some of its
pitfalls. First, we note that standard model-based clustering likely leads to
the same number of clusters per margin, which seems a rather artificial
assumption for a variety of datasets. We tackle this issue by specifying a
finite mixture model per margin that allows each margin to have a different
number of clusters, and then cluster the multivariate data using a strategy
game-inspired algorithm to which we call Reign-and-Conquer. Second, since the
proposed clustering approach only specifies a model for the margins -- but
leaves the joint unspecified -- it has the advantage of being partially
parallelizable; hence, the proposed approach is computationally appealing as
well as more tractable for moderate to high dimensions than a `full' (joint)
model-based clustering approach. A battery of numerical experiments on
artificial data indicate an overall good performance of the proposed methods in
a variety of scenarios, and real datasets are used to showcase their
application in practice.
