Walrasian Dynamics in Multi-unit Markets.

In a multi-unit market, a seller brings multiple units of a good and tries tosell them to a set of buyers that have monetary endowments. While a Walrasianequilibrium does not always exist in this model, natural relaxations of theconcept that retain its desirable fairness properties do exist.

We study the dynamics of (Walrasian) envy-free pricing mechanisms in thisenvironment, showing that for any such pricing mechanism, the best responsedynamic starting from truth-telling converges to a pure Nash equilibrium withsmall loss in revenue and welfare. Moreover, we generalize these bounds tocapture all the Nash equilibria for a large class of (monotone) pricingmechanisms. We also identify a natural mechanism, which selects the minimumWalrasian envy-free price, in which for $n=2$ buyers the best response dynamicconverges from any starting profile, and for which we conjecture convergencefor any number of buyers.