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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 payoffs
Assume an Npersons game where each player i has a payoff function f_i(X). X is the joint strategy of all players. So payoff function f_i depends on the ith 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 payoff 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 bestreply mechanism. 

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coinciding, convergence, nash, optima, payoffs 
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