The study of the set of Nash equilibrium points for one two-players game with quadratic payoff functions

Authors

  • Mikhail Sergeevich Nikolskii Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
  • Aboubacar Moussa Department of Mathematics and Computer Science, Faculty of Sciences, Abdou Moumouni University, Niamey, Niger

DOI:

https://doi.org/10.2298/YJOR130917012N

Keywords:

two-players game, Nash equilibrium, quadratic payoff functions

Abstract

In this paper, the general two-players game on the square with quadratic payoff functions is considered. We have studied the problem of determination of the set of Nash equilibrium points, and here we present a constructive graphical method for determination of the required set which we have developed.

References

Parhasarathi, T., and Raghavan, T., Some questions of the theory of two-person games, M.: Mir, 1974. (in Russian)

Petrosyan, L.A., Zenkevich, N.A., and Semina, E.A., Game theory, M.: High School, 1998. (in Russian)

Vasin, A.A., and Morozov, V.V., Introduction to game theory with applications to economics, M.: 2003. (in Russian)

Maschenko, S.O., “The concept of Nash equilibrium and its development (review)”, Journal of Comput. and Appl. Mathematics, 1(107) (2012) 40-65. (in Russian)

Zhukovsky, V.I., Introduction to differential games with uncertainty. Nash equilibrium, M., KRASAND, 2010. (in Russian)

Aubin, J.P., Nonlinear analysis and its economic application, M.: Mir, 1988. (in Russian)

Rosen, J. B., “Existence and uniqueness of equilibrium points for concave N-person games”, Econometrica, 33(3) (1965) 520-534.

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Published

2015-06-01

Issue

Vol. 25 No. 2 (2015)

Section

Research Articles

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