Regret, stability & fairness in matching markets with bandit learners

TL;DR

This paper demonstrates that in competitive matching markets with learning agents, it is possible to achieve stability, fairness, low regret, and high social welfare simultaneously by incorporating costs and transfers, challenging previous impossibility results.

Contribution

The paper introduces a model with costs and transfers in competitive matching markets, showing that four desirable properties can coexist, unlike prior models suggesting trade-offs.

Findings

Achieving stability, fairness, low regret, and high welfare simultaneously is possible.

Incorporating costs and transfers overcomes previous impossibility results.

The model provides a more optimistic outlook for long-term outcomes in competitive markets.

Abstract

Making an informed decision -- for example, when choosing a career or housing -- requires knowledge about the available options. Such knowledge is generally acquired through costly trial and error, but this learning process can be disrupted by competition. In this work, we study how competition affects the long-term outcomes of individuals as they learn. We build on a line of work that models this setting as a two-sided matching market with bandit learners. A recent result in this area states that it is impossible to simultaneously guarantee two natural desiderata: stability and low optimal regret for all agents. Resource-allocating platforms can point to this result as a justification for assigning good long-term outcomes to some agents and poor ones to others. We show that this impossibility need not hold true. In particular, by modeling two additional components of competition -- namely, costs and transfers -- we prove that it is possible to simultaneously guarantee four desiderata: stability, low optimal regret, fairness in the distribution of regret, and high social welfare.