Joint Pricing and Matching for Resource Allocation Platforms via Min-cost Flow Problem

TL;DR

This paper introduces a method to optimize pricing strategies in resource allocation platforms by modeling the problem as a min-cost flow, accounting for probabilistic matching and achieving a (1-1/e)-approximation.

Contribution

It formulates the joint pricing and matching problem as a min-cost flow problem and develops an approximation algorithm for it.

Findings

Provides a (1-1/e)-approximation algorithm for the problem.

Models the pricing and matching problem as a convex min-cost flow.

Addresses the challenge of non-convexity and hard-to-evaluate objectives.

Abstract

Stochastic matching is the stochastic version of the well-known matching problem, which consists in maximizing the rewards of a matching under a set of probability distributions associated with the nodes and edges. In most stochastic matching problems, the probability distributions inherent in the nodes and edges are set a priori and are not controllable. However, many resource allocation platforms can control the probability distributions by changing prices. For example, a rideshare platform can control the distribution of the number of requesters by setting the fare to maximize the reward of a taxi-requester matching. Although several methods for optimizing price have been developed, optimizations in consideration of the matching problem are still in its infancy. In this paper, we tackle the problem of optimizing price in the consideration of the resulting bipartite graph matching, given the effect of the price on the probabilistic uncertainty in the graph. Even though our problem involves hard to evaluate objective values and is non-convex, we construct a (1-1/e)-approximation algorithm under the assumption that a convex min-cost flow problem can be solved exactly.