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arXiv · 1712.08910

Walrasian Dynamics in Multi-unit Markets

Simina Brânzei·Aris Filos-Ratsikas
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Abstract

In a multi-unit market, a seller brings multiple units of a good and tries to sell them to a set of buyers that have 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 mechanisms in this environment, showing that for any such pricing mechanism, the best response dynamic starting from truth-telling 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 mechanisms. We also identify a natural mechanism, which selects the minimum Walrasian envy-free price, in which for $n=2$ buyers the best response dynamic converges from any starting profile, and for which we conjecture convergence for any number of buyers.

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Simina Brânzei, Aris Filos-Ratsikas. 2018-09-27. Walrasian Dynamics in Multi-unit Markets. https://arxiv.org/abs/1712.08910

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