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Matching and pricing are two critical levers in two-sided marketplaces toconnect demand and supply. The platform can produce more efficient matching andpricing decisions by batching the demand requests. We initiate the study of thetwo-stage stochastic matching problem, with or without pricing, to enable theplatform to make improved decisions in a batch with an eye toward the imminentfuture demand requests. This problem is motivated in part by applications inonline marketplaces such as ride hailing platforms.  We design online competitive algorithms for vertex-weighted (or unweighted)two-stage stochastic matching for maximizing supply efficiency, and two-stagejoint matching and pricing for maximizing market efficiency. In the formerproblem, using a randomized primal-dual algorithm applied to a family of``balancing'' convex programs, we obtain the optimal $3/4$ competitive ratioagainst the optimum offline benchmark. Using a factor revealing program andconnections to submodular optimization, we improve this ratio against theoptimum online benchmark to $(1-1/e+1/e^2)\approx 0.767$ for the unweighted and$0.761$ for the weighted case. In the latter problem, we design optimal$1/2$-competitive joint pricing and matching algorithm by borrowing ideas fromthe ex-ante prophet inequality literature. We also show an improved$(1-1/e)$-competitive algorithm for the special case of demand efficiencyobjective using the correlation gap of submodular functions. Finally, wecomplement our theoretical study by using DiDi's ride-sharing dataset forChengdu city and numerically evaluating the performance of our proposedalgorithms in practical instances of this problem.

Two-stage Stochastic Matching and Pricing with Applications to Ride Hailing