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Respond to the question: Existance of euilibrium in Nplayer game?

11/28/2005 06:36 AM by Nick; Existance of euilibrium in N-player game

Consider a game of N players. Each player has two strategies A and B.
The pay-off of A is K (a constant >0). The pay-off of B if f(m), a function of the number of players who choose strategy A. f is a fairly complated function but we know that is is monotonic, i.e. f(i+1)>f(i) for all 0<=i<=N. We also know that f(0)=0 and f(N)>K. So the best outcome for any indiviual player is that everybody else chooses A and he/she chooses B.

What can be said about the existance of an equilibrium in this game?

I am a theoretical physicist (PhD in string theory) but with very limited experience of Game Theory.

I would be grateful for an answer. [Manage messages]