Geodesic
Monotonicity of the mapping associated with a noncooperative multiperson game
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 9, pp. 1554-1564

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A noncooperative multiperson game can be associated with a mapping that generates a variational inequality. The problem of searching for Nash points in the game is equivalent to solving this inequality. Numerical methods for solving the variational inequality rely heavily on the monotonicity of the mapping generating the inequality. At the same time, the mapping associated with the noncooperative multiperson game may not be monotone. Necessary and sufficient conditions are established under which the mapping associated with a finite noncooperative mixed-strategy game of three or more persons is monotone. 
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     author = {E. G. Gol'shtein},
     title = {Monotonicity of the mapping associated with a~noncooperative multiperson game},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1554--1564},
     publisher = {mathdoc},
     volume = {49},
     number = {9},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_9_a1/}
}
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E. G. Gol'shtein. Monotonicity of the mapping associated with a noncooperative multiperson game. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 9, pp. 1554-1564. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_9_a1/