Online two-sided markets: many buyers enhance learning

Anna Lunghi, Matteo Castiglioni, Alberto Marchesi

Keywords: online learning, bilateral trade, mechanism design, theory

Abstract:

We study repeated trading problems involving a *single seller* and *multiple buyers*. We generalize classical bilateral trade mechanisms by introducing a second-price auction among the buyers before proposing a price to the seller.
This setup increases competition and reveals more information about buyers' valuations, resulting in an *informational advantage* over bilateral trade. However, the seller still makes a binary accept/reject decision, resulting in *asymmetric feedback*.
We show that this richer feedback model enables us to overcome known lower bounds in the single-buyer case. Specifically, we achieve a $\tilde{O}(T^{2/3})$ regret bound against the best *strong budget-balanced* mechanism, without assumptions on value distributions.
Furthermore, when either *(i)* the valuations of the buyers and the seller are independent or *(ii)* they are sampled from bounded density distributions, we achieve a $\tilde{O}(T^{2/3})$ regret bound against *global budget-balanced* mechanisms.

Submission Number: 211