Online Market Equilibrium with Application to Fair Division
Yuan Gao, Christian Kroer, Alex Peysakhovich

TL;DR
This paper introduces an online market equilibrium concept and a scalable dynamic algorithm called PACE for fair division in sequential markets, demonstrating asymptotic convergence to desirable equilibrium properties.
Contribution
It proposes a novel online market equilibrium framework with PACE dynamics, extending to quasilinear utilities and providing the first online algorithm for first-price pacing equilibria.
Findings
PACE converges asymptotically to market equilibrium.
Properties like no envy and Pareto optimality are achieved online.
Numerical experiments show rapid convergence.
Abstract
Computing market equilibria is a problem of both theoretical and applied interest. Much research to date focuses on the case of static Fisher markets with full information on buyers' utility functions and item supplies. Motivated by real-world markets, we consider an online setting: individuals have linear, additive utility functions; items arrive sequentially and must be allocated and priced irrevocably. We define the notion of an online market equilibrium in such a market as time-indexed allocations and prices which guarantee buyer optimality and market clearance in hindsight. We propose a simple, scalable and interpretable allocation and pricing dynamics termed as PACE. When items are drawn i.i.d. from an unknown distribution (with a possibly continuous support), we show that PACE leads to an online market equilibrium asymptotically. In particular, PACE ensures that buyers'…
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Taxonomy
TopicsAdvanced Bandit Algorithms Research · Optimization and Search Problems · Mobile Crowdsensing and Crowdsourcing
