Fair Online Bilateral Trade

TL;DR

This paper studies fair pricing in online bilateral trade, proposing a fairness measure based on equal utility sharing, and characterizes the regret bounds under different learning scenarios and information settings.

Contribution

It introduces a fairness criterion for online trade, analyzes regret bounds for various information regimes, and highlights limitations of utility-maximizing algorithms under fairness constraints.

Findings

Deterministic setting achieves $ heta( ext{ln} T)$ regret.

Stochastic setting with independent valuations has $ ilde{ heta}(T^{2/3})$ regret.

Full valuation observation allows for tight regret bounds.

Abstract

In online bilateral trade, a platform posts prices to incoming pairs of buyers and sellers that have private valuations for a certain good. If the price is lower than the buyers' valuation and higher than the sellers' valuation, then a trade takes place. Previous work focused on the platform perspective, with the goal of setting prices maximizing the gain from trade (the sum of sellers' and buyers' utilities). Gain from trade is, however, potentially unfair to traders, as they may receive highly uneven shares of the total utility. In this work we enforce fairness by rewarding the platform with the fair gain from trade, defined as the minimum between sellers' and buyers' utilities. After showing that any no-regret learning algorithm designed to maximize the sum of the utilities may fail badly with fair gain from trade, we present our main contribution: a complete characterization of the regret regimes for fair gain from trade when, after each interaction, the platform only learns whether each trader accepted the current price. Specifically, we prove the following regret bounds: $\Theta(\ln T)$ in the deterministic setting, $\Omega(T)$ in the stochastic setting, and $\tilde{\Theta}(T^{2/3})$ in the stochastic setting when sellers' and buyers' valuations are independent of each other. We conclude by providing tight regret bounds when, after each interaction, the platform is allowed to observe the true traders' valuations.