Title: The efficiency analysis for oligopolistic games when cost functions are non-separable

Authors: Deren Han, Hai Yang, Xiaoming Yuan

Addresses: School of Mathematical Sciences, Nanjing Normal University, Nanjing 210097, P.R. China. ' Department of Civil Engineering, The Hong Kong University of Science and Technology, Clear Water bay, Kowloon, Hong Kong. ' Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

Abstract: By deriving an upper bound of the so-called |price of anarchy|, this paper analyses the efficiency of oligopolistic games in networks with non-separable and asymmetric cost functions, splittable flows and fixed demands. The new bound is determined by the optimal objective function values of some optimisation problems. In particular, for some special cases, the bound turns out to be explicit in the sense that it is representable explicitly by the number of players, and the constants measuring the degree of asymmetry and non-linearity of the cost function.

Keywords: oligopolistic games; price of anarchy; PoA; non-separable; equilibrium; system optimum; optimisation; cost functions; splittable flows; fixed demands.

DOI: 10.1504/IJMMNO.2010.031751

International Journal of Mathematical Modelling and Numerical Optimisation, 2010 Vol.1 No.3, pp.237 - 257

Published online: 22 Feb 2010 *

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