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.
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Grigorieva, E.V., Khailov, E.N. Hierarchical differential game between manufacturer, retailer, and bank. J Dyn Control Syst 15, 359–391 (2009). https://doi.org/10.1007/s10883-009-9069-9
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DOI: https://doi.org/10.1007/s10883-009-9069-9