We consider a model whereby players compete for a set of shared resources to produce and sell substitute products in the same market, which can be viewed as a generalization of the classical Cournot oligopolistic competition model, or, from a different angle, the Wardrop type routing model. In particular, we suppose that there are K players, who compete for the usage of resources as well as the sales of the end-products. Moreover, the unit costs of the shared resources and the selling prices of the products are assumed to be affine linear functions in the consumption/production quantities. We show that the price of anarchy in this case is lower bounded by 1/K, and this bound is essentially tight, which manifests the harsh nature of the competitive market for the producers.
Bibliographical noteFunding Information:
Acknowledgments Simai He received research support from City University of Hong Kong 7200207 and RGC Earmarked Grant CityU 143711; Xiaoguo Wang and Shuzhong Zhang received support from RGC Earmarked Grant CUHK419409.
- Cournot oligopoly competition
- Nash equilibrium
- Price of anarchy