Walrasian Dynamics in Multi-Unit Markets


  • Simina Brânzei Purdue University
  • Aris Filos-Ratsikas Ecole Polytechnique Fédérale de Lausanne




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 (reasonable) 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. We conjecture convergence of the mechanism for any number of buyers and provide simulation results to support our conjecture.




How to Cite

Brânzei, S., & Filos-Ratsikas, A. (2019). Walrasian Dynamics in Multi-Unit Markets. Proceedings of the AAAI Conference on Artificial Intelligence, 33(01), 1812-1819. https://doi.org/10.1609/aaai.v33i01.33011812



AAAI Technical Track: Game Theory and Economic Paradigms