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Math Help - convergence to Nash equilibrium that coincides with global optima of pay-offs

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    convergence to Nash equilibrium that coincides with global 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 find some sufficient conditions for convergence for these kind of games.
    Last edited by Torck; May 29th 2008 at 02:59 PM.
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