Geodesic
Split of an Optimization Variable in Game Theory
R. Aboulaich1 ; A. Habbal2 ; N. Moussaid1
1 LERMA, E.M.I., Avenue Ibn Sina B.P 765, Agdal, Rabat. Morocco
2 LJAD, University of Nice Sophia-Antipolis, Valrose, 06108 Nice Cedex 2, France
Mathematical modelling of natural phenomena, Tome 5 (2010) no. 7 Supplement, pp. 122-127.

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In the present paper, a general multiobjective optimization problem is stated as a Nash game. In the nonrestrictive case of two objectives, we address the problem of the splitting of the design variable between the two players. The so-called territory splitting problem is solved by means of an allocative approach. We propose two algorithms in order to find fair allocation tables
DOI : 10.1051/mmnp/20105720

R. Aboulaich 1 ; A. Habbal 2 ; N. Moussaid 1

1 LERMA, E.M.I., Avenue Ibn Sina B.P 765, Agdal, Rabat. Morocco
2 LJAD, University of Nice Sophia-Antipolis, Valrose, 06108 Nice Cedex 2, France 
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R. Aboulaich; A. Habbal; N. Moussaid. Split of an Optimization Variable in Game Theory. Mathematical modelling of natural phenomena, Tome 5 (2010) no. 7 Supplement, pp. 122-127. doi : 10.1051/mmnp/20105720. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20105720/

[1] J. P. Aubin. Mathematical methods of game and economic theory. North-Holland Publishing Co. Amsterdam, New York, 1979.

[2] A. Habbal A topology Nash game for tumoral antangiogenesis Struct. Multidisc. Optim. 2005 404 412

[3] A. Habbal, J. Petersson, M. Thellner Multidisciplinary topology optimization solved as a Nash game Struct. Multidisc. Optim. 2004 949 963

[4] J. A. Désidéri. Split of territories in concurrent optimization. Rapport de recherche, INRIA, 2007.

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