Existence of anonymous link tolls for decentralizing an oligopolistic game and the efficiency analysis

Pages: 347 - 364, Volume 7, Issue 2, May 2011

doi:10.3934/jimo.2011.7.347       Abstract        References        Full Text (392.6K)       Related Articles

Deren Han - School of Mathematical Sciences and Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing 210046, China (email)
Xiaoming Yuan - Department of Mathematics, Hong Kong Baptist University, Hong Kong, China (email)

Abstract: To apply the traditional marginal-cost pricing to drive a user equilibrium of the oligopolistic game to the system optimum, it requires to classify the users into different classes and then charge discriminatory tolls across user classes. By realizing the difficulty of discriminating users when they differ in some unobservable ways, Yang and Zhang investigated existence of anonymous link tolls for transportation networks recently. In this paper, we consider the anonymous link tolls for the oligopolistic game with nonseparable, nonlinear and asymmetric cost functions with fixed demands. With similar techniques developed by Yang and Zhang, we first prove the existence of anonymous link tolls to decentralize the system optimum to a user equilibrium. Then, by deriving some bounds on the so-called price of anarchy, we analyze the efficiency of such a toll strategy when the tolls are considered as part of the system cost.

Keywords:  Anonymous link tolls, Oligopolistic games, User equilibrium, System optimum, Price of anarchy, Asymmetric cost functions.
Mathematics Subject Classification:  Primary: 58F15, 58F17; Secondary: 53C35.

Received: January 2010;      Revised: January 2011;      Published: April 2011.

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