Sets of Pareto–Nash Equilibria in Dyadic Two-Criterion Mixed-Strategy Games

  • Valeriu UngureanuEmail author
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 89)


In this chapter, the notion of Pareto–Nash equilibrium is investigated as a continuation of the precedent chapter as well as a continuation of prior works (Sagaidac and Ungureanu, Operational research, CEP USM, Chişinău, 296 pp, 2004 (in Romanian), [1]; Ungureanu, Comp Sci J Moldova, 14(3(42)):345–365, 2006, [2]; Ungureanu, ROMAI J, 4(1):225–242, 2008, [3]). First, problems and needed basic theoretical results are exposed. The method of intersection of graphs of best response mappings presented above and initiated in Ungureanu (Comp Sci J Moldova, 14(3(42)):345–365, 2006, [2]) is applied to solve dyadic two-criterion mixed-strategy games. To avoid misunderstanding, some previous results, which are applied in this chapter, are briefly exposed, too.


  1. 1.
    Sagaidac, M., and V. Ungureanu. 2004. Operational Research. Chişinău: CEP USM, 296 pp. (in Romanian).Google Scholar
  2. 2.
    Ungureanu, V. 2006. Nash equilibrium set computing in finite extended games. Computer Science Journal of Moldova 14 (3(42)): 345–365.Google Scholar
  3. 3.
    Ungureanu, V. 2008. Solution principles for simultaneous and sequential games mixture. ROMAI Journal 4 (1): 225–242.MathSciNetzbMATHGoogle Scholar
  4. 4.
    Selten, R. 1975. Reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory 4 (1): 22–55.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Borm, P., F. Van Megen, and S. Tijs. 1999. A perfectness concept for multicriteria games. Mathematical Methods of Operations Research 49 (3): 401–412.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Yu, H. 2003. Weak Pareto equilibria for multiobjective constrained games. Applied Mathematics Letters 16: 773–776.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Podinovskii, V.V., and V.D. Nogin. 1982. Pareto-optimal solutions of the multi-criteria problems. Moscow: Nauka, 255 pp. (in Russian).Google Scholar
  8. 8.
    Jahn, J. 2004. Vector Optimization: Theory, Applications and Extensions, Series Operations Research. Berlin: Springer, XV+481 pp.Google Scholar
  9. 9.
    Lozan, V., and V. Ungureanu. 2009. Principles of Pareto-Nash equilibrium. Studia Universitatis 7: 52–56.Google Scholar
  10. 10.
    Lozan, V., and V. Ungureanu. 2011. Pareto–Nash equilibria in bicriterial dyadic games with mixed strategies, Wolfram Demonstrations Project. Accessed 13 Oct 2011.

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceMoldova State UniversityChișinăuMoldova

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