A Computational Method for Solving $N$-Person Game
The nonzero sum $n$-person game has been considered. It is well known that the game can be reduced to a global optimization problem [5; 7; 14]. By extending Mills’ result [5], we derive global optimality conditions for a Nash equilibrium. In order to solve the problem numerically, we apply the Curvi...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Irkutsk State University
2017-06-01
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| Series: | Известия Иркутского государственного университета: Серия "Математика" |
| Subjects: | |
| Online Access: | http://isu.ru/journal/downloadArticle?article=_ff2b225b5d8c4bd989ba608294a24820&lang=eng |
| Summary: | The nonzero sum $n$-person game has been considered. It is well known that the game can be reduced to a global optimization problem [5; 7; 14]. By extending Mills’ result [5], we derive global optimality conditions for a Nash equilibrium. In order to solve the problem numerically, we apply the Curvilinear Multistart Algorithm [2; 3] developed for finding global solutions in nonconvex optimization problems. The proposed algorithm was tested on three and four person games. Also, for the test purpose, we have considered competitions of 3 companies at the bread market of Ulaanbaatar as the three person game and solved numerically. |
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| ISSN: | 1997-7670 2541-8785 |