Improved Online Contention Resolution for Matchings and Applications to the Gig Economy
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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 (i j) ∈ E in any order and make a one-time take-it-or-leave-it offer of a price π_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 1/2(1-e^-2)≈ 0.432 of [BGMS21], 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 OCRS 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.
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