Split of an Optimization Variable in Game Theory

R. Aboulaich; A. Habbal; N. Moussaid

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 7, page 122-127
  • ISSN: 0973-5348

Abstract

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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

How to cite

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Aboulaich, R., Habbal, A., and Moussaid, N.. Taik, A., ed. "Split of an Optimization Variable in Game Theory." Mathematical Modelling of Natural Phenomena 5.7 (2010): 122-127. <http://eudml.org/doc/197632>.

@article{Aboulaich2010,
abstract = {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},
author = {Aboulaich, R., Habbal, A., Moussaid, N.},
editor = {Taik, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {multiobjective optimization; concurrent optimization; split of territories; Nash equilibrium; Pareto front},
language = {eng},
month = {8},
number = {7},
pages = {122-127},
publisher = {EDP Sciences},
title = {Split of an Optimization Variable in Game Theory},
url = {http://eudml.org/doc/197632},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Aboulaich, R.
AU - Habbal, A.
AU - Moussaid, N.
AU - Taik, A.
TI - Split of an Optimization Variable in Game Theory
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/8//
PB - EDP Sciences
VL - 5
IS - 7
SP - 122
EP - 127
AB - 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
LA - eng
KW - multiobjective optimization; concurrent optimization; split of territories; Nash equilibrium; Pareto front
UR - http://eudml.org/doc/197632
ER -

References

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  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., 30 (2005), 404–412. 
  3. A. Habbal, J. Petersson, M. Thellner. Multidisciplinary topology optimization solved as a Nash game. Struct. Multidisc. Optim., 61 (2004), 949–963. 
  4. J. A. Désidéri. Split of territories in concurrent optimization. Rapport de recherche, INRIA, 2007.  

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