  In this work we present and analyze a fluid-mechanical model of competition
(scavenging) amongst $N$ liquid droplets (individual competitors). The eventual
outcome of this competition depends sensitively on the average resource
(volume) per individual $\overline{V}$. For abundant resource,
$\overline{V}>1$, there is one winner only and that winner eventually scavenges
all or most of the resource. In the socio-economic realm this is is known as
the "winner-take-all" outcome: A disproportionately large reward falls to one
or a few winners, even though other competitors start out with comparable (or
even slightly more) resource and perform only marginally worse. The losing
competitors are not rewarded. For less than abundant resource,
$\overline{V}<1$, an outcome with resource that is evenly partitioned amongst
the $N$ droplets becomes possible. This is the "all-share-evenly" or
egalitarian outcome. For sufficiently scarce resource the egalitarian outcome
is the only one that can occur. In addition to predicting what kind and how
many winners, our analysis shows that once an individual's resource (droplet
volume) falls below a fixed threshold, that individual can neither recover nor
emerge as winner. This is the "once down-and-out, always down-and-out" outcome.
Selected simulations suggest that the winner depends sensitively on population
size and the "trading friction" or inefficiency of resource exchange between
individuals (liquid rheology). Of all feasible rest states (equilibria), only
certain ones are reachable (stable equilibria). Friction turns out to strongly
influence the time to reach an end state (stable equilibrium), in surprising
ways. Besides the end states, our analysis reveals an array of rest states,
ordered in hierarchies of more versus less costly (energetic) outcomes.
