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This paper targets at service provisioning and bandwidth allocation in single-service overlay multicast network by modeling it as a first-price monopoly auction. We propose a game theoretic pricing mechanism for determining the distribution of a typical multimedia content from an origin server, via the unicast links. By leveraging the rich theory of strategic mechanism design of microeconomics, we formulate this problem as an optimization problem that aims to achieve Nash equilibrium for bidding strategy of the buyers. In our proposal, the content of the multimedia service accounts for the good. The sellers of this auction economy are either the origin server or the peers who forward the multimedia service to their downstream peers. For each seller, its corresponding downstream peers play the role of buyers who are referred to as bidders. Each bidder submits a sealed bid to its corresponding seller. The high bidder wins and pays its bid for the service. The analytical and experimental results prove the efficiency of the proposed mechanism in terms of the overlay path stretch.