  We introduce and study analytically and numerically a simple model of
inter-agent competition, where underachievement is strongly discouraged. We
consider $N\gg 1$ particles performing independent Brownian motions on the
line. Two particles are selected at random and at random times, and the
particle closest to the origin is reset to it. We show that, in the limit of
$N\to \infty$, the dynamics of the coarse-grained particle density field can be
described by a nonlocal hydrodynamic theory which was encountered in a study of
the spatial extent of epidemics in a critical regime. The hydrodynamic theory
predicts relaxation of the system toward a stationary density profile of the
"swarm" of particles, which exhibits a power-law decay at large distances. An
interesting feature of this relaxation is a non-stationary "halo" around the
stationary solution, which continues to expand in a self-similar manner. The
expansion is ultimately arrested by finite-$N$ effects at a distance of order
$\sqrt{N}$ from the origin, which gives an estimate of the average radius of
the swarm. The hydrodynamic theory does not capture the behavior of the
particle farthest from the origin -- the current leader. We suggest a simple
scenario for typical fluctuations of the leader's distance from the origin and
show that the mean distance continues to grow indefinitely as $\sqrt{t}$.
Finally, we extend the inter-agent competition from $n=2$ to an arbitrary
number $n$ of competing Brownian particles ($n\ll N$). Our analytical
predictions are supported by Monte-Carlo simulations.
