On a generalized Cournot oligopolistic competition game

  • Authors:

  • Simai He;Xiaoguo Wang;Shuzhong Zhang

  • Affiliations:

  • Department of Management Sciences, City University of Hong Kong, Kowloon Tong, Hong Kong;Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong;Industrial and Systems Engineering Program, University of Minnesota, Minneapolis, USA 55455

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2013

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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.