Improved Online Contention Resolution for Matchings and Applications to the Gig Economy

Motivated by applications in the gig economy, we study approximation algorithms for a sequential pricing problem. The input is a bipartite graph $G=(I,J,E)$ between individuals I and jobs J. The platform has a value of v_j for matching job j to an individual worker. In order to find a matching, the platform can consider the edges $(ij)\in E$ in any order and make a one-time take-it-or-leave-it offer of a price ${\pi }_{ij}=w$ of its choosing to i for completing j. The worker accepts the offer with a known probability p_ijw; in this case, the job and the worker are irrevocably matched. What is the best way to make offers to maximize revenue and/or social welfare? The optimal algorithm is known to be NP-hard to compute (even if there is only a single job). With this in mind, we design efficient approximations to the optimal policy via a new random-order online contention resolution scheme (RO-OCRS) for matching. Our main result is a 0.456-balanced RO-OCRS in bipartite graphs and a 0.45-balanced RO-OCRS in general graphs. These algorithms improve on the recent bound of $\frac{1}{2}(1-{\mathtt{e}}^{-2})\approx 0.432$ and improve on the best-known lower bounds for the correlation gap of matching, despite applying to a significantly more restrictive setting. As a consequence of our online contention resolution scheme results, we obtain a 0.456-approximate algorithm for the sequential pricing problem. We further extend our results to settings where workers can only be contacted a limited number of times and show how to achieve improved results for this problem via improved algorithms for the well-studied stochastic probing problem.

Funding: This work was supported by the National Science Foundation [Grant CCF2209520] and a gift from Amazon Research.