My Math Forum convergence to Nash coinciding with optima of pay-offs

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 May 29th, 2008, 06:41 AM #1 Newbie   Joined: May 2008 Posts: 2 Thanks: 0 convergence to Nash coinciding with optima of pay-offs Assume an N-persons game where each player i has a pay-off function f_i(X). X is the joint strategy of all players. So pay-off function f_i depends on the i-th player's strategy and on the strategies of the other players. (Strategy sets are continuous). Now assume that there exists a Nash equilibrium X* so that EACH player is in a global maximum of its pay-off function. (this means there exists an X* for which f_i(X*)=max f_i(X) for all i) Does this case exist somewhere in literature? I would like to proof that this kind of games always converge when using a best-reply mechanism.

 Tags coinciding, convergence, nash, optima, payoffs

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