Online service platforms have transformed how customers and suppliers connect in real-time, using centralized dispatch and pricing systems. However, by acting as "central planners", platforms risk undermining the workers' flexibility endorsed by the gig economy. Hence, there has been significant scrutiny on the classification of gig workers as independent contractors and their freedom in decisions that directly influence their earnings, such as prices. To alleviate such concerns, several platforms in the ride-hailing industry have adopted or tested decentralized pricing schemes, where workers set prices flexibly. However, this approach presents a complex trade-off. On the one hand, platforms' pricing systems enable an efficient matching process by balancing demand and supply. Individual suppliers' pricing decisions may overlook market-wide effects on supply-demand equilibrium. On the other hand, suppliers possess private information about their preferences and costs that platforms cannot easily infer and use for price discrimination. Decentralized pricing can accommodate supplier-side heterogeneity, potentially increasing workers' participation in the market.

Motivated by centralized matching markets, we study an online stochastic matching problem on edge-weighted graphs, where the agents' arrivals and abandonments are stochastic and heterogeneous. The problem is formulated as a continuous-time Markov decision process (MDP) under the average-cost criterion. While the MDP is computationally intractable, we design simple matching algorithms that achieve constant-factor approximations in cost-minimization and reward-maximization settings. Specifically, we devise a 3-approximation algorithm for cost minimization on graphs satisfying a metric-like property. We develop a (e-1)/(2e)-approximation algorithm for reward maximization on arbitrary bipartite graphs. Our algorithms possess a greedily-like structure informed by fluid relaxations. In extensive experiments, we simulate the matching operations of a car-pooling platform using real-world taxi demand data. The newly-developed algorithms have the potential to significantly improve cost efficiency in certain market conditions against the widely used batching algorithms.