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On a generalized Cournot oligopolistic competition game

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Abstract

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.

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Authors and Affiliations

  1. Department of Management Sciences, City University of Hong Kong, Kowloon Tong, Hong Kong

    Simai He

  2. Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong

    Xiaoguo Wang

  3. Industrial and Systems Engineering Program, University of Minnesota, Minneapolis, MN, 55455, USA

    Shuzhong Zhang

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  1. Simai He
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  2. Xiaoguo Wang
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  3. Shuzhong Zhang
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Correspondence to Shuzhong Zhang.

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Shuzong Zhang—on leave from Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong.

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He, S., Wang, X. & Zhang, S. On a generalized Cournot oligopolistic competition game. J Glob Optim 56, 1335–1345 (2013). https://doi.org/10.1007/s10898-012-9844-0

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