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Mathematical Problems in Engineering
Volume 2015, Article ID 721970, 10 pages
http://dx.doi.org/10.1155/2015/721970
Research Article

Infinity Period Dynamic Control of a Kind of Channel’s Price and Brand Investment: A Differential Game Method

1School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, China
2Research Center for Social Work Development, Southwestern University of Finance and Economics, Chengdu 610074, China

Received 22 November 2014; Accepted 20 January 2015

Academic Editor: Honglei Xu

Copyright © 2015 Kaihong Wang 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.

Abstract

The infinity period dynamic control problem of distribution channel was studied with differential game approach. Four differential dynamic control models of coordinated channel game, uncoordinated static game, Stackelberg game with manufacture controlled, and Stackelberg game with retailers controlled were constructed. Some results applied dynamic optimization theory made with Hamilton function. The conclusions are as follows. (1) Optimization brand investment controlled by manufacture has nothing to do with time. (2) Retail price was the most minimum when channel was integrated. (3) Manufacture’s profits of uncoordinated static game and Stackelberg game with manufacture controlled were more than Stackelberg game with retailers controlled. (4) Retailer’s profits of Stackelberg game with retailers controlled were less than Stackelberg game with manufacture controlled. (5) Channel’s total profits of Stackelberg game with retailers controlled were the most minimum.