International Journal of Game Theory

, Volume 8, Issue 1, pp 13–25 | Cite as

Uniqueness of equilibrium points in bimatrix games

  • G. A. Heuer


Bimatrix games are constructed having a given pair (x, y) as the unique equilibrium point within the class of all mixed strategy pairs whose nonzero components are the same as (resp., among) those of (x, y). In each case, necessary and sufficient conditions on (x, y) for the existence of such a game are obtained. All games having the first property are constructed. The work extends and complements recent (separate) works ofMillham [1972],Raghavan [1970] and the author. The methods and results are valid in the context of any ordered field.


Equilibrium Point Economic Theory Game Theory Mixed Strategy Nonzero Component 
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  1. Balinski, M.L.: An algorithm for finding all vertices of convex polyhedral sets. J. Soc. Indust. Appl. Math.9, 1961, 72–88.Google Scholar
  2. Eaves, B.C.: The linear complementarity problem. Management Sci.17, 1971, 612–634.Google Scholar
  3. Heuer, G.A.: On completely mixed strategies in bimatrix games. J. London Math. Soc.11 (2), 1975, 17–20.Google Scholar
  4. Kuhn, H. W.: An algorithm for equilibrium points in bimatrix games. Proc. Nat. Acad. Sci. USA47, 1961, 1657–1662.Google Scholar
  5. Lemke, C.E., andJ.T. Howson, Jr.: Equilibrium points of bimatrix games. J. Soc. Indust. Appl. Math.12, 1964, 413–423.Google Scholar
  6. Mangasarian, O.L.: Equilibrium points of bimatrix games. J. Soc. Indust. Appl. Math.12, 1964, 778–780.Google Scholar
  7. Mangasarian, O., andH. Stone: Two-person nonzero-sum games and quadratic programming. J. Math. Anal. Appl.9, 1964, 348–355.Google Scholar
  8. Millham, C.B.: Constructing bimatrix games with special properties. Naval Res. Logist. Quart.19, 1972, 709–714.Google Scholar
  9. Mills, H.: Equilibrium points in finite games. J. Soc. Indust. Appl. Math.8, 1960, 397–402.Google Scholar
  10. Nash, J.F.: Non-cooperative games. Ann. of Math.54, 1951, 286–295.Google Scholar
  11. Raghavan, T.E.S.: Completely mixed strategies in bimatrix games. J. London Math. Soc.2 (2), 1970, 709–712.Google Scholar
  12. Shapley, L.S.: A note on the Lemke-Howson algorithm. Math. Programming Stud.1, 1974, 175–189.Google Scholar

Copyright information

© Physica-Verlag 1979

Authors and Affiliations

  • G. A. Heuer
    • 1
  1. 1.Department of Mathematics and Computer ScienceConcordia CollegeMoorheadUSA

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