No Access

Existence of Equilibrium Points for Bimatrix Game with Interval Payoffs

Ajay Kumar Bhurjee

Department of Mathematics, National Institute of Science & Technology, Palur Hills, Berhampur, Odisha-761008, India

E-mail Address: ajaybhurjee1984@gmail.com

https://doi.org/10.1142/S021919891650002XCited by:3 (Source: Crossref)

Abstract

This paper deals a bimatrix game with payoffs as closed intervals. Existence of equilibrium point of this game is discussed by using suitable interval quadratic programming problem. Further, a methodology is proposed for finding optimal strategies for each player of the game. The methodology is illustrated by numerical example.

Keywords:

AMSC: 91A05, 91A10, 91A80, 90C20

References

Akyar, E., Akyar, H. D. and Düzce, S. A. [2011] Brown–Robinson method for interval matrix games, Soft Comput. 15(10), 2057–2064. Crossref, Web of Science, Google Scholar
Bhurjee, A. and Panda, G. [2012] Efficient solution of interval optimization problem, Math. Methods Oper. Res. 76(3), 273–288. Crossref, Web of Science, Google Scholar
Collins, W. D. and Hu, C. [2008] Studying interval valued matrix games with fuzzy logic, Soft Comput. 12(2), 147–155. Crossref, Web of Science, Google Scholar
Gao, J. [2013] Uncertain bimatrix game with applications, Fuzzy Optim. Decis. Making 12(1), 65–78. Crossref, Web of Science, Google Scholar
Hladík, M. [2010] Interval valued bimatrix games, Kybernetika 46(3), 435–446. Web of Science, Google Scholar
Li, D. F. [2011] Linear programming approach to solve interval-valued matrix games, Omega 39(6), 655–666. Crossref, Web of Science, Google Scholar
Liu, S. T. and Kao, C. [2009] Matrix games with interval data, Comput. Ind. Eng. 56(4), 1697–1700. Crossref, Web of Science, Google Scholar
Nash, J. [1950] Equilibrium points in $n$ $n$ -person games, Proc. Natl. Acad. Sci. 36(1), 48–49. Crossref, Web of Science, Google Scholar
Nash, J. [1951] Non-cooperative games, Ann. Math. 54(2), 286–295. Crossref, Web of Science, Google Scholar
Rosen, J. B. [1965] Existence and uniqueness of equilibrium points for concave $n$ $n$ -person games, Econometrica 33(3), 520–534. Crossref, Web of Science, Google Scholar
Von Neumann, L. J. and Morgenstern, O. [1947] Theory of Games and Economic Behavior (Princeton University Press Princeton, NJ). Google Scholar