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Nash Equilibria in Pure Strategies
Author(s) -
Ziad Abderrahmane
Publication year - 2003
Publication title -
bulletin of economic research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.227
H-Index - 29
eISSN - 1467-8586
pISSN - 0307-3378
DOI - 10.1111/1467-8586.00178
Subject(s) - mathematical economics , nash equilibrium , strategy , best response , economics , epsilon equilibrium , zero sum game , variable (mathematics) , mathematics , zero (linguistics) , function (biology) , space (punctuation) , mathematical optimization , game theory , computer science , mathematical analysis , linguistics , philosophy , evolutionary biology , biology , operating system
We consider an n ‐person non‐zero‐sum non‐cooperative game in normal form, where the strategy sets are some closed intervals of the real line. It is shown that if the pay‐off functions are continuous on the whole space and if for each pay‐off function the smallest local maximum in the strategy variable is a global maximum, then the game possesses a pure strategy Nash equilibrium.