  Single-file transport, where particles cannot bypass each other, has been
observed in various experimental setups. In such systems, the behaviour of a
tracer particle (TP) is subdiffusive, which originates from strong correlations
between particles. These correlations are especially marked when the TP is
driven and leads to inhomogeneous density profiles. Determining the impact of
this inhomogeneity when several TPs are driven in the system is a key question,
related to the general issue of bath-mediated interactions, which are known to
induce collective motion and lead to the formation of clusters or lanes in a
variety of systems. Quantifying this collective behaviour, the emerging
interactions and their dependence on the amplitude of forces driving the TPs,
remains a challenging but largely unresolved issue. Here, considering dense
single-file systems, we analytically determine the entire dynamics of the
correlations and reveal out of equilibrium cooperativity and competition
effects between driven TPs.
