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This paper shows that in suitable markets, even with out-of-equilibrium tradeallowed, a simple price update rule leads to rapid convergence toward theequilibrium. In particular, this paper considers a Fisher market repeated overan unbounded number of time steps, with the addition of finite sized warehousesto enable non-equilibrium trade. The main result is that suitable tatonnementstyle price updates lead to convergence in a significant subset of marketssatisfying the Weak Gross Substitutes property. Throughout this process thewarehouse are always able to store or meet demand imbalances (the neededcapacity depends on the initial imbalances). Finally, our price update rule isrobust in a variety of regards: 1. The updates for each good depend only oninformation about that good (its current price, its excess demand since itslast update) and occur asynchronously from updates to other prices. 2. Theprocess is resilient to error in the excess demand data. 3. Likewise, theprocess is resilient to discreteness, i.e. a limit to divisibility, both ofgoods and money.

Discrete Price Updates Yield Fast Convergence in Ongoing Markets with Finite Warehouses