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Journal of Applied Mathematics
Volume 2013, Article ID 480962, 9 pages
Research Article

A Game-Theoretic Analysis of Bandwidth Allocation under a User-Grouping Constraint

1Department of Electrical Engineering, National Chung Hsing University, 250 Kuo-Kuang Road, Taichung 402, Taiwan
2Department of Law and Graduate Institute of Technology Management, National Chung Hsing University, 250 Kuo-Kuang Road, Taichung 402, Taiwan

Received 2 October 2012; Revised 22 December 2012; Accepted 26 December 2012

Academic Editor: Xiaoning Zhang

Copyright © 2013 Shun-Pin Hsu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new bandwidth allocation model is studied in this paper. In this model, a system, such as a communication network, is composed of a finite number of users, and they compete for limited bandwidth resources. Each user adopts the decision that maximizes his or her own benefit characterized by the utility function. The decision space of each user is subject to constraints. In addition, some users form a group, and their joint decision space is also subject to constraints. Under the assumption that each user’s utility function satisfies some continuity and concavity conditions, the existence, uniqueness, and fairness, in some appropriate sense, of the Nash equilibrium point in the allocation game are proved. An algorithm yielding a sequence converging to the equilibrium point is proposed. Finally, a numerical example with detailed analysis is provided to illustrate the effectiveness of our work.