Algebraic Hyper-Structures Associated to Nash Equilibrium Point and Applications

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A. Delavar Khalafi, B. Davvaz, Algebraic Hyper-Structures Associated to Nash Equilibrium Point and Applications, Int. J. Anal. Appl., 14 (1) (2017), 20-26.

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A. Delavar Khalafi, B. Davvaz

Abstract

In this paper, we generalize some concepts of the game theory such as Nash equilibrium point, saddle point and existence theorems on hyper-structures. Based on new definitions and theorems, we obtain some important results in the game theory. A few suitable examples have been given for better understanding.

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References

  1. P. Corsini, Prolegomena of Hypergroup Theory, Second edition, Aviani Editore, 1993.
  2. P. Corsini and V. Leoreanu, Applications of Hyperstructure Theory, Advances in Mathematics, Kluwer Academic Publishers, Dordrecht, 2003.
  3. I. Cristea and M. Stefanescu, Hypergroups and n-ary relations, Eur. J. Comb. 31 (2010), 780-789.
  4. B. Davvaz, A. Dehghan Nezhad and A. Benvidi, Chemical hyperalgebra: Dismutation reactions, MATCH Commun. Math. Comput. Chem. 67 (2012) 55-63.
  5. B. Davvaz, A. Dehghan Nezhad and A. Benvidi, Chain reactions as experimental examples of ternary algebraic hyperstructures, MATCH Commun. Math. Comput. Chem. 65 (2011) 491-499.
  6. B. Davvaz and V. Leoreanu-Fotea, Hyperring Theory and Applications, International Academic Press, USA, 2007.
  7. A. Dehghan Nezhad and B. Davvaz, Universal hyperdynamical systems, Bull. Korean Math. Soc. 47 (2010), 513-526.
  8. A. Delavar Khalafi and B.Davvaz, Algebraic hyper-structures associated to convex analysis and applications, Filomat 26 (2012) 55-65.
  9. A. Delavarkhalafi Solution methods for equilibrium points in bileaner non-zero sum games, Ph.D. Thesis (2002) (In Russian).
  10. M. Ghadiri, B. Davvaz and R. Nekouian, H v -Semigroup structure on F 2 -offspring of a gene pool, Int. J. Biomath. 5 (2012), Art. ID 1250011.
  11. S. Hoˇ sková and J. Chvalina, Discrete transformation hypergroups and transformation hypergroups with phase tolerance space, Discre. Math. 308 (2008), 4133-4143.
  12. V. Leoreanu-Fotea, B. Davvaz, Fuzzy hyperrings, Fuzzy Sets and Syst. 160 (2009), 2366-2378.
  13. T. Vougiouklis, Hyperstructures and Their Representations, Hadronic Press, Florida, 1994.