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Game theory - A Tutorial |
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Static: General Results |
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Here are some of the key results of the theory of static games. Theorem 1 (John Nash) [3] A finite static game always has at least one Nash equilibrium, possibly mixed. |
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A finite game is one with finitely many players who all have a finite number of possible choices. The proof of the result uses Kakutani’s fixed point theorem.
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Theorem 2 (Rosen) [4] A concave static game always has at least one pure Nash equilibrium. |
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A convex game is one where the players choose a sub-vector xi of a vector x (that is some of the components of x) so that the resulting vector x is in a convex set. Moreover, the payoff of player i is continuous in x and concave in xi. |
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John Nash |