Geodesic
A Generalized Model of Hierarchically Controlled Dynamical System
Contributions to game theory and management, Tome 2 (2009), pp. 320-333.

Voir la notice de l'article provenant de la source Math-Net.Ru

The idea of the paper is to combine in the same model several concepts from game theory, graph theory, and controlled dynamical systems theory, namely: 1) a directed graph without contours and loops; 2) a game of $n$ players in normal form; 3) a cooperative game; 4) a dynamical system controlled by several subjects. The combination permits to describe complex dynamical systems with hierarchical structure (particularly organizational and environmental systems) more completely and to take into consideration different interactive and interdependent aspects of the systems. Some examples are considered such as environmental control, corruption modeling, and linear multistage games with hierarchical matrices.
Keywords: hierarchical game theory, directed graphs, controlled dynamical systems. 
@article{CGTM_2009_2_a25,
     author = {Guennady A. Ougolnitsky},
     title = {A {Generalized} {Model} of {Hierarchically} {Controlled} {Dynamical} {System}},
     journal = {Contributions to game theory and management},
     pages = {320--333},
     publisher = {mathdoc},
     volume = {2},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2009_2_a25/}
}
TY  - JOUR
AU  - Guennady A. Ougolnitsky
TI  - A Generalized Model of Hierarchically Controlled Dynamical System
JO  - Contributions to game theory and management
PY  - 2009
SP  - 320
EP  - 333
VL  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CGTM_2009_2_a25/
LA  - en
ID  - CGTM_2009_2_a25
ER  - 
%0 Journal Article
%A Guennady A. Ougolnitsky
%T A Generalized Model of Hierarchically Controlled Dynamical System
%J Contributions to game theory and management
%D 2009
%P 320-333
%V 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CGTM_2009_2_a25/
%G en
%F CGTM_2009_2_a25
Guennady A. Ougolnitsky. A Generalized Model of Hierarchically Controlled Dynamical System. Contributions to game theory and management, Tome 2 (2009), pp. 320-333. http://geodesic.mathdoc.fr/item/CGTM_2009_2_a25/

[1] Bac M., “Corruption and Supervision Costs in Hierarchies”, Comparative Economics, 22 (1996) | Zbl

[2] Bardhan P., “Corruption and Development: a Review of Issues”, J. Political Economy, 31 (1996)

[3] Gavrilov V. M., Optimal Processes in Conflict Situations, Sovetskoe Radio, M., 1969, in Russian pp. | Zbl

[4] Denin K. I., “A Two-level Game-theoretical Hierarchical Model of Plural Corruptive Interaction”, GTM 2008 Abstracts, 2008, 36–38

[5] Klitgaard R., Gifts and Bribes. Strategy and Choice, MIT Press, Cambridge, 1991

[6] Levin M. I., Zirik M. L., “Corruption as an Object of Mathematical Modeling”, Economics and Mathematical Methods, 34:3 (1998) (in Russian) | Zbl

[7] Ougolnitsky G. A., The Linear Theory of Hierarchical Systems, Preprint, Institute of Systems Analysis, M., 1996 (in Russian)

[8] Ougolnitsky G. A., “Game Theoretic Modeling of the Hierarchical Control of Sustainable Development”, Game Theory and Applications, 8 (2002), 82–91 | MR

[9] Ougolnitsky G. A., “Game Theoretic Modeling of the Hierarchical Control of Sustainable Development”, Computer Modeling. Ecology, v. 2, Vuzovskaya Kniga, M., 2004, 101–125 (in Russian)

[10] Rose-Ackerman S., “Corruption and Development”, Annual Bank Conference on Development Economics, 1997

[11] Rybasov E. A., Ougolnitsky G. A., “Mathematical Modeling of the Ecological-Economic Systems with Hierarchical Structure Considering Corruption”, Computer Modeling. Ecology, v. 2, Vuzovskaya Kniga, M., 2004, 46–65 (in Russian)