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The sharing of scarce resources among multiple rational agents is one of theclassical problems in economics. In exchange economies, which are used to modelsuch situations, agents begin with an initial endowment of resources andexchange them in a way that is mutually beneficial until they reach acompetitive equilibrium (CE). The allocations at a CE are Pareto efficient andfair. Consequently, they are used widely in designing mechanisms for fairdivision. However, computing CEs requires the knowledge of agent preferenceswhich are unknown in several applications of interest. In this work, we explorea new online learning mechanism, which, on each round, allocates resources tothe agents and collects stochastic feedback on their experience in using thatallocation. Its goal is to learn the agent utilities via this feedback andimitate the allocations at a CE in the long run. We quantify CE behavior viatwo losses and propose a randomized algorithm which achieves sublinear lossunder a parametric class of utilities. Empirically, we demonstrate theeffectiveness of this mechanism through numerical simulations.

Learning Competitive Equilibria in Exchange Economies with Bandit Feedback