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Extensive research in recent years has shown the benefits of cooperative relaying in wireless networks, where nodes overhear and cooperatively forward packets transmitted between their neighbors. Most existing studies focus on physical-layer optimization of the effective channel capacity for a given transmitter-receiver link; however, the interaction among simultaneous flows between different endpoint pairs, and the conflicts arising from their competition for a shared pool of relay nodes, are not yet well understood. In this paper, we study a distributed pricing framework, where sources pay relay nodes to forward their packets, and the payment is shared equally whenever a packet is successfully relayed by several nodes at once. We formulate this scenario as a Stackelberg (leader-follower) game, in which sources set the payment rates they offer, and relay nodes respond by choosing the flows to cooperate with. We provide a systematic analysis of the fundamental structural properties of this generic model. We show that multiple follower equilibria exist in general due to the nonconcave nature of their game, yet only one equilibrium possesses certain continuity properties that further lead to a unique system equilibrium among the leaders. We further demonstrate that the resulting equilibria are reasonably efficient in several typical scenarios.