  The stable allocation problem is one of the broadest extensions of the
well-known stable marriage problem. In an allocation problem, edges of a
bipartite graph have capacities and vertices have quotas to fill. Here we
investigate the case of uncoordinated processes in stable allocation instances.
In this setting, a feasible allocation is given and the aim is to reach a
stable allocation by raising the value of the allocation along blocking edges
and reducing it on worse edges if needed. Do such myopic changes lead to a
stable solution?
  In our present work, we analyze both better and best response dynamics from
an algorithmic point of view. With the help of two deterministic algorithms we
show that random procedures reach a stable solution with probability one for
all rational input data in both cases. Surprisingly, while there is a
polynomial path to stability when better response strategies are played (even
for irrational input data), the more intuitive best response steps may require
exponential time. We also study the special case of correlated markets. There,
random best response strategies lead to a stable allocation in expected
polynomial time.
