An Analytic Method for Interval Bimatrix Games
An Analytic Method for Interval Bimatrix Games
摘要
This paper deals with rnxn two-person non-zero sum games with interval pay-offs. An analytic method for solving such games is given. A pair of Nash Equilibrium is found by using the method. The analytic method is effective to find at least one Nash Equilibrium (N.E) for two-person bimatrix games. Therefore, the analytic method for two-person bimatrix games is adapted to interval bimatrix games.
参考文献11
-
1C. Lemke and J. Howson Jr., Equilibrium points of bimatrix games, Journal of the Society for Industrial and Applied Mathematics vol.12, no.2, (1964) 413-423.
-
2J. Nash, Non-Cooperative Games, Annals of Mathematics, Vol.54, No.2, 1951.
-
3Owen G., Game Theory Third Edition Academic Press (1995). R.E.Moore, Methods and Applications of Interval Analysis, SIAM, Philadelphia, USA, 1979.
-
4H. Akyar, E.Akyar, A Graphical Method for Interval Matrix Games, Abstract and Applied Analysis, 2011 doi: 10. I 155/2011/260490.
-
5D.W.Collins and C.Hu, Studying interval valued matrix games with fuzzy logic, Soft Computing, vol.12, no.2, pp. 147-155, 2008.
-
6P.K. Nayak and M.Pal, The bi-matrix games with interval payoffs and its Nash equilibrium strategy, Journal of Fuzzy Mathematics, vol. 17, no.2, pp.421-435, 2009.
-
7A.Sengupta, T.K.Pal, and D.Chakraborty, Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming, Fuzzy Sets and Systems, vol.119, no.l, pp.129-138, 2001.
-
8P.K.Nayak and M.Pal, Solution of rectangular interval games using graphical method, Tamsui Oxford Journal of Mathematical Sciences, vol,22, no.l, pp.95-115, 2006.
-
9A.Sengupta and T.K.Pal, On comparing interval numbers, European Journal of Operational Research 127 (2000) 28-43.
-
10L.V.Koloba~kina, Osnovm Teorii |gr, M.; BiNOM. Laboratiriya znaniy, 2011.
-
1孙毓平,吴江航.THE STABILITY AND CONVERGENCE OF THE FINITE ANALYTIC METHOD FOR THE NUMERICAL SOLUTION OF CONVECTIVE DIFFUSION EQUATION[J].Applied Mathematics and Mechanics(English Edition),1989,10(6):521-528.
-
2纪振义,叶开沅.A HIGH CONVERGENT PRECISION EXACT ANALYTIC METHOD FOR DIFFERENTIAL EQUATION WITH VARIABLE COEFFICIENTS[J].Applied Mathematics and Mechanics(English Edition),1993,14(3):201-207.
-
3纪振义,叶开源.EXACT ANALYTIC METHOD FG(?) SOLVING VARIABLE COEFFICIENT DIFFERENTIAL EQUATION[J].Applied Mathematics and Mechanics(English Edition),1989,10(10):885-896.
-
4廖世俊.HOMOTOPY ANALYSIS METHOD: A NEW ANALYTICMETHOD FOR NONLINEAR PROBLEMS[J].Applied Mathematics and Mechanics(English Edition),1998,19(10):957-962.
-
5叶开源,纪振义.AN EXACT ANALYTIC METHOD APPLIED TO NONHOMOGENEOUS RING-AND STRINGER-STIFFENED CYLINDRICAL SHELLS[J].Applied Mathematics and Mechanics(English Edition),1989,10(9):785-796.
-
6SIU Yum-Tong.Finite generation of canonical ring by analytic method[J].Science China Mathematics,2008,51(4):481-502.
-
7Chen Daoqiof Math., Zhejiang Univ., Hangzhou, 310027..EXTENSIONS OF SOME INEQUALITIES[J].Applied Mathematics(A Journal of Chinese Universities),2001,16(3):241-243. 被引量:2
-
8ZHOU Yu-Qing,ZONG Hong-Shi,FENG Hong-Tao.Analytic Method to Study Influence of Finite Chemical Potential in QED_3~*[J].Communications in Theoretical Physics,2009,52(11):909-913.
-
9陈芳,刘青泉.Modified asymptotic Adomian decomposition method for solving Boussinesq equation of groundwater flow[J].Applied Mathematics and Mechanics(English Edition),2014,35(4):481-488. 被引量:2
-
10张世雄.ACCURATE COMPUTATION AND INTERPOLATION TECHNIQUE OF FINITE ANALYTIC COEFFICIENTS[J].Applied Mathematics and Mechanics(English Edition),1992,13(5):437-444.