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Selfish overlay networks consist of autonomous nodes that develop their own strategies by optimizing towards their local objectives and self-interests, rather than following prescribed protocols. It is thus important to regulate the behavior of selfish nodes, so that system-wide properties are optimized. In this paper, we investigate the problem of bandwidth allocation in overlay networks, and propose to use a market-driven approach to regulate the behavior of selfish nodes that either provide or consume services. In such markets, consumers of services select the best service providers, taking into account both the performance and the price of the service. On the other hand, service providers are encouraged to strategically decide their respective prices in a pricing game, in order to maximize their economic revenues and minimize losses in the long run. In order to overcome the limitations of previous models towards similar objectives, we design a decentralized algorithm that uses reinforcement learning to help selfish nodes to incrementally adapt to the local market, and to make optimized strategic decisions based on past experiences. We have simulated our proposed algorithm in randomly generated overlay networks, and have shown that the behavior of selfish nodes converges to their optimal strategies, and resource allocations in the entire overlay are near-optimal, and efficiently adapts to the dynamics of overlay networks.