Hierarchical differential games between manufacturer and retailer

Pages: 300 - 314, Issue Special, September 2009

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Ellina Grigorieva - Department of Mathematics and Computer Sciences, Texas Woman's University, Denton, TX 76204, United States (email)
Evgenii Khailov - Department of Computer Mathematics and Cybernetics, Moscow State Lomonosov University, Moscow, 119992, Russian Federation (email)

Abstract: 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:  Optimal Control, Game Theory, Economic Models
Mathematics Subject Classification:  49J15, 58E25, 90A16, 93B03

Received: July 2008;      Revised: February 2009;      Published: September 2009.