Hierarchical differential games between manufacturer and retailer

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2009, 2009(Special): 300-314. doi: 10.3934/proc.2009.2009.300

Hierarchical differential games between manufacturer and retailer

Ellina Grigorieva ^1, and Evgenii Khailov ^2,

1.	Department of Mathematics and Computer Sciences, Texas Woman's University, Denton, TX 76204
2.	Department of Computer Mathematics and Cybernetics, Moscow State Lomonosov University, Moscow, 119992

Received July 2008 Revised February 2009 Published September 2009

Abstract
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A two-dimensional microeconomic model with three bounded controls is created and investigated. The model describes a manufacturer producing a consumer good and a retailer that buys this product in order to resell it for a profit. Two types of differential hierarchical games will be applied in order to model the interactions between the manufacturer and retailer. We will consider the difficult case in which the maximum of the objective functions can be reached only on the boundary of the admissible set. Optimal strategies for manufacturer and retailer in both games will be found. The object of our interest is the investigation of the vertical integration of retail and industrial groups. We will determine the conditions of interaction that produce a stable and maximally effective structure over given planning periods.

Keywords: Economic Models, Optimal Control, Game Theory.

Mathematics Subject Classification: 49J15, 58E25, 90A16, 93B03.

Citation: Ellina Grigorieva, Evgenii Khailov. Hierarchical differential games between manufacturer and retailer. Conference Publications, 2009, 2009 (Special) : 300-314. doi: 10.3934/proc.2009.2009.300

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