Stability is essential for long term sustainability of supply chain networks. The literature on supply chain coordination focuses on enhancing network efficiency, and stability issues are largely unexplored. In this paper, we consider a two-tier supply chain network with a marketing agent coordinating activities among the network players using a price and profit sharing based coordination mechanism. Our non-cooperative game theoretic model shows that a unique subgame perfect Nash equilibrium exists that facilitates development of structural results characterizing network stability from the perspectives of costs, number of players and parameters of the coordination mechanism. In particular, we obtain ranges for cost, number of players and the profit sharing parameter over which the network is internally and/or externally stable. Our results suggest that cooperation among the network players is not always necessary; network efficiency can be achieved in some situations with the coordination mechanism adopted here.