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Most existing overlay multicast proposals have assumed that the nodes are cooperative and thus focus on the global topology optimization. However, a unique and important characteristic of overlay nodes is that, as application-layer agents, they can be selfish with their own interests. To achieve better quality-of-service (QoS) or to minimize forwarding overhead, an overlay node can behave selfishly in the information collection or in the overlay construction. While the former has recently been investigated, the impact of selfishness in the construction action remains unclear. In this paper, we present the first systematic study on the impact of selfishness in both tree and mesh overlay construction. Our investigation considers multiple QoS measures for streaming applications, including stream latency, resolution, and continuity. Our contribution is twofold: first, we analyze how for selfish overlay nodes to choose a construction-action policy to optimize their individual multi-metric QoS. Second, we demonstrate that the selfishness-aware policy for the construction action is consistent with the QoS optimization for the global multicast session, but not vice versa. The implication is significant: A globally optimal overlay construction itself can be vulnerable to individual selfishness; but, following our directions, we can design an overlay that is both globally optimal and selfish-resistant.