Structure of equilibria in N-person non-cooperative games

Chin, H. H. ; Parthasarathy, T. ; Raghavan, T. E. S. (1974) Structure of equilibria in N-person non-cooperative games International Journal of Game Theory, 3 (1). pp. 1-19. ISSN 0020-7276

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Here we study the structure of Nash equilibrium points for N-person games. For two-person games we observe that exchangeability and convexity of the set of equilibrium points are synonymous. This is shown to be false even for three-person games. For completely mixed games we get the necessary inequality constraints on the number of pure strategies for the players. Whereas the equilibrium point is unique for completely mixed two-person games, we show that it is not true for three-person completely mixed game without some side conditions such as convexity on the equilibrium set. It is a curious fact that for the special three-person completely mixed game with two pure strategies for each player, the equilibrium point is unique; the proof of this involves some combinatorial arguments.

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ID Code:36512
Deposited On:05 Jul 2011 10:41
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