International Journal of Game Theory

, Volume 8, Issue 2, pp 65–79 | Cite as

On equilibria in finite games

  • V. Bubelis


We are concerned with Nash equilibrium points forn-person games. It is proved that, given any real algebraic numberα, there exists a 3-person game with rational data which has a unique equilibrium point andα is the equilibrium payoff for some player. We also present a method which allows us to reduce an arbitraryn-person game to a 3-person one, so that a number of questions about generaln-person games can be reduced to consideration of the special 3-person case. Finally, a completely mixed game, where the equilibrium set is a manifold of dimension one, is constructed.


Rational Data Nash Equilibrium Equilibrium Point Economic Theory Game Theory 
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Copyright information

© Physica-Verlag 1979

Authors and Affiliations

  • V. Bubelis
    • 1
  1. 1.Lithuanian Academy of SciencesVilniusUSSR

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