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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bubelis, V.: A Note on Structure of Equilibrium Point in Finite Non-Cooperative Games. Mathematical Methods in Social Sciences4, 1974, 37–42 (Russian).Google Scholar
  2. —: A Game with no Basic Equilibrium points. Mathematical Methods in Social Sciences7, 1976a, 9–16 (Russian).Google Scholar
  3. -: Relation of Non-Cooperative N-Person Games to Three-Person Games. Contemporary Directions in Game Theory. Ed. by E. Vilkas and A. Korbut. Vilnius 1976, 18–24 (Russian).Google Scholar
  4. Chin, H.H., T. Parthasarathy, andT.E.S. Raghavan: Structure of Equilibria inN-Person Non-Cooperative Games. Int. J. Game Theory3, 1974, 1–19.Google Scholar
  5. Gale, D., H.W. Kuhn, andA.W. Tucker: On Symmetric Games. Contributions to the Theory of Games, I. Ed. by H.W. Kuhn and A.W. Tucker. Princeton 1950, 81–87.Google Scholar
  6. Lemke, C.E., andJ.T. Howson: Equilibrium Points in Bimatrix Games. SIAM J. Appl. Math.12, 1964, 413–423.Google Scholar
  7. Nash, J.F., andL.S. Shapley: A Simple Three-Person Poker Game. Contributions to the Theory of Games, I. Ed. by H.W. Kuhn and A.W. Tucker. Princeton 1950, 105–116.Google Scholar

Copyright information

© Physica-Verlag 1979

Authors and Affiliations

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

Personalised recommendations