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This paper articulates a dynamic model of price-based network revenue management, where a set of service providers are involved in oligopolistic competition that is equilibrium tending. The service providers are price setters whose price setting strategies induce time lagged impacts on demand. The price setting mechanisms of these providers resemble the replicator dynamics that are common to evolutionary games. This paper shows that the resulting Cournot-Nash game takes the form of a differential variational inequality. Existence results are provided and an abstract numerical example is solved via a fixed point algorithm that may be implemented with offthe-shelf software. Suggested extensions of the model are also provided.

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