  This paper shows that in suitable markets, even with out-of-equilibrium trade
allowed, a simple price update rule leads to rapid convergence toward the
equilibrium. In particular, this paper considers a Fisher market repeated over
an unbounded number of time steps, with the addition of finite sized warehouses
to enable non-equilibrium trade. The main result is that suitable tatonnement
style price updates lead to convergence in a significant subset of markets
satisfying the Weak Gross Substitutes property. Throughout this process the
warehouse are always able to store or meet demand imbalances (the needed
capacity depends on the initial imbalances). Finally, our price update rule is
robust in a variety of regards: 1. The updates for each good depend only on
information about that good (its current price, its excess demand since its
last update) and occur asynchronously from updates to other prices. 2. The
process is resilient to error in the excess demand data. 3. Likewise, the
process is resilient to discreteness, i.e. a limit to divisibility, both of
goods and money.
