Joint Pricing and Matching for Resource Allocation Platforms via Min-cost Flow Problem
arxiv(2024)
摘要
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.
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