Walrasian Dynamics in Multi-unit Markets

In a multi-unit market, a seller brings multiple units of a good and tries to sell them to a set of buyers equipped with monetary endowments. While a Walrasian equilibrium does not always exist in this model, natural relaxations of the concept that retain its desirable fairness properties do exist. We study the dynamics of (Walrasian) envy-free pricing algorithms in this environment, showing that for any such pricing algorithm, the best response dynamic process converges to a pure Nash equilibrium with small loss in revenue and welfare. Moreover, we generalize these bounds to capture all the Nash equilibria for a large class of (monotone) pricing algorithms.