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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 9, Pages 1554–1564 (Mi zvmmf4747)  

This article is cited in 1 scientific paper (total in 1 paper)

Monotonicity of the mapping associated with a noncooperative multiperson game

E. G. Gol'shtein

Central Institute of Mathematical Economics, Russian Academy of Sciences, Nakhimovskii pr. 47, Moscow, 117418, Russia

Abstract: 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.

Key words: noncooperative multiperson game, monotone mapping, variational inequality, numerical solution of variational inequalities.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:9, 1483–1492

Bibliographic databases:

UDC: 519.626+519.83
Received: 26.12.2008

Citation: E. G. Gol'shtein, “Monotonicity of the mapping associated with a noncooperative multiperson game”, Zh. Vychisl. Mat. Mat. Fiz., 49:9 (2009), 1554–1564; Comput. Math. Math. Phys., 49:9 (2009), 1483–1492

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Golshtein E.G., “O modifikatsiyakh konechnoi beskoalitsionnoi igry, imeyuschikh vypukluyu strukturu”, Ekonomika i matematicheskie metody, 46:4 (2010), 101–107  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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