Hierarchical differential game between manufacturer, retailer, and bank

Authors:
E. V. Grigorieva;E. N. Khailov
Affiliations:
Department of Mathematics and Computer Sciences, Texas Woman's University, Denton, USA 76204;Department of Computer Mathematics and Cybernetics, Moscow State Lomonosov University, Moscow, Russia 119991
Venue:
Journal of Dynamical and Control Systems
Year:
2009

Citing 6
Cited 0

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Abstract

In this work, a microeconomic model describing interactions between a manufacturer, retailer and bank is created and investigated. The manufacturer produces a single product, the retailer buys the good in order to resell it to the third party for a profit, and the bank lends the money. For the first time, a non-cooperative hierarchical game approach will be applied to a three-dimensional model with five bounded controls. The best optimal strategy for each player will be found analytically with the use of the Pontryagin Maximum Principle. A simulation software package is developed to demonstrate the performance of our proposed optimal algorithms.