Research Article
Algebraic Hyper-Structures Associated to Nash Equilibrium Point and Applications
- Yazd University
* Corresponding author
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.
How to Cite
A. Delavar Khalafi, B. Davvaz, Algebraic Hyper-Structures Associated to Nash Equilibrium Point and Applications, Int. J. Anal. Appl. 14 (2017), 20–26.
BibTeX
@article{Khalafi2017,
author = {Delavar Khalafi, A. and Davvaz, B.},
title = {Algebraic Hyper-Structures Associated to Nash Equilibrium Point and Applications},
journal = {Int. J. Anal. Appl.},
volume = {14},
year = {2017},
pages = {20--26},
doi = {}
}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.