Nash Equilibria for Noncooperative n -Person Games in Normal Form

S.H. Tijs

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Game Theory and Applications Game Theory and Voting Systems Fixed Point Theorems Analysis

Abstract

This paper concentrates on the problem of the existence of $\varepsilon $-equilibrium points in the Nash sense for noncooperative n-person games in normal form. Firstly, a survey of known $\varepsilon $-equilibrium.point theorems and proof techniques is given. Then various new $\varepsilon $-equilibrium point theorems are derived, in which one of the players has a big strategy space and where nonbounded, payoff functions are allowed. To prove these theorems, results of Arzela–Ascoli are extended.

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References

1950Equilibrium points in n -person games 1951Non-Cooperative Games 1965Existence and Uniqueness of Equilibrium Points for Concave N-Person Games 1928Zur Theorie der Gesellschaftsspiele 1952A Social Equilibrium Existence Theorem*1964Equilibrium Points of Bimatrix Games 1978Oligopoly and the Theory of Games.1955Note on non-cooperative convex game

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