'SIMPLE' STABILITY OF GENERAL N-PERSON GAMES.
PRINCETON UNIV N J ECONOMETRIC RESEARCH PROGRAM
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Three different notes are presented here which are related to certain new and simple concepts of non-cooperative n-person games. These are natural generalizations of the notions of maximin and minimax strategies and the saddle points of two-person games. The concept of the equilibrium point appears as a special case of one of these. The first note expresses some intuitive considerations for games on Euclidean spaces. Their characterizations are essentially given by Kakutanis fixed point theorem. As a particular case, we examine such points for the mixed extensions of finite n-person games. The second and third notes are concerned with two different mathematical extensions of the results obtained in the first note. They are based respectively on Fans and Nikaido-Isodas ideas of proving the existence of equilibrium points for games on real linear topological spaces. In particular, the concepts introduced in the first note are examined for mixed extensions of continuous games. These last two notes involve the use of more advanced mathematical techniques than does the first.
- Theoretical Mathematics