Skip to main content
Erschienen in: Soft Computing 10/2011

01.10.2011 | Original Paper

Brown–Robinson method for interval matrix games

verfasst von: Emrah Akyar, Handan Akyar, Serkan Ali Düzce

Erschienen in: Soft Computing | Ausgabe 10/2011

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper, two-person interval matrix games are considered, and by means of acceptability index, Brown–Robinson method to find a mixed-strategy equilibrium is adapted to interval matrix games. Numerical examples are also given.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Brown GW (1949) Some notes on computation of games solutions. RAND Report P-78, The Rand Corporation, Santa Monica Brown GW (1949) Some notes on computation of games solutions. RAND Report P-78, The Rand Corporation, Santa Monica
Zurück zum Zitat Dwayne Collins W, Hu C (2008) Studying interval valued matrix games with fuzzy logic. Soft Comput 12(2):147–155MATHCrossRef Dwayne Collins W, Hu C (2008) Studying interval valued matrix games with fuzzy logic. Soft Comput 12(2):147–155MATHCrossRef
Zurück zum Zitat Ishibuchi H, Tanaka H (1990) Multiobjective programming in optimization of the interval objective function. Eur J Oper Res 48(2):219–225MATHCrossRef Ishibuchi H, Tanaka H (1990) Multiobjective programming in optimization of the interval objective function. Eur J Oper Res 48(2):219–225MATHCrossRef
Zurück zum Zitat Kundu S (1997) Min-transitivity of fuzzy leftness relationship and its application to decision making. Fuzzy Sets Syst 86(3):357–367MathSciNetMATHCrossRef Kundu S (1997) Min-transitivity of fuzzy leftness relationship and its application to decision making. Fuzzy Sets Syst 86(3):357–367MathSciNetMATHCrossRef
Zurück zum Zitat Kurano M, Yasuda M, Nakagami Ji, Yoshida Y (2002) An interval matrix game and its extensions to fuzzy and stochastic games. S\(\bar{\hbox{u}}\)rikaisekikenky\(\bar{\hbox{u}}\)sho K\(\bar{\hbox{o}}\)ky\(\bar{\hbox{u}}\)roku (1263):103–116 Kurano M, Yasuda M, Nakagami Ji, Yoshida Y (2002) An interval matrix game and its extensions to fuzzy and stochastic games. S\(\bar{\hbox{u}}\)rikaisekikenky\(\bar{\hbox{u}}\)sho K\(\bar{\hbox{o}}\)ky\(\bar{\hbox{u}}\)roku (1263):103–116
Zurück zum Zitat Moore RE (1979) Methods and applications of interval analysis, SIAM Studies in Applied Mathematics, vol 2. Society for Industrial and Applied Mathematics (SIAM), Philadelphia Moore RE (1979) Methods and applications of interval analysis, SIAM Studies in Applied Mathematics, vol 2. Society for Industrial and Applied Mathematics (SIAM), Philadelphia
Zurück zum Zitat Nakahara Y, Sasaki M, Gen M (1992) On the linear programming problems with interval coefficients. Comput Ind Eng 23(1-4):301–304CrossRef Nakahara Y, Sasaki M, Gen M (1992) On the linear programming problems with interval coefficients. Comput Ind Eng 23(1-4):301–304CrossRef
Zurück zum Zitat Nayak PK, Pal M (2006) Solution of rectangular interval games using graphical method. Tamsui Oxf J Math Sci 22(1):95–115MathSciNetMATH Nayak PK, Pal M (2006) Solution of rectangular interval games using graphical method. Tamsui Oxf J Math Sci 22(1):95–115MathSciNetMATH
Zurück zum Zitat Nayak PK, Pal M (2009) Linear programming technique to solve two person matrix games with interval pay-offs. Asia Pac J Oper Res 26(2):285–305MathSciNetMATHCrossRef Nayak PK, Pal M (2009) Linear programming technique to solve two person matrix games with interval pay-offs. Asia Pac J Oper Res 26(2):285–305MathSciNetMATHCrossRef
Zurück zum Zitat Okada S, Gen M (1994) Order relation between intervals and its application to shortest path problem. Jpn J Fuzzy Theory Syst 6(6):703–717 Okada S, Gen M (1994) Order relation between intervals and its application to shortest path problem. Jpn J Fuzzy Theory Syst 6(6):703–717
Zurück zum Zitat Robinson J (1951) An iterative method of solving a game. Ann Math 2(54):296–301CrossRef Robinson J (1951) An iterative method of solving a game. Ann Math 2(54):296–301CrossRef
Zurück zum Zitat Sengupta A, Pal TK (2009) Fuzzy preference ordering of interval numbers in decision problems. Studies in Fuzziness and Soft Computing, vol 238. Springer, Berlin Sengupta A, Pal TK (2009) Fuzzy preference ordering of interval numbers in decision problems. Studies in Fuzziness and Soft Computing, vol 238. Springer, Berlin
Zurück zum Zitat Sengupta A, Pal TK, Chakraborty D (2001) Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming. Fuzzy Sets Syst 119(1):129–138 Sengupta A, Pal TK, Chakraborty D (2001) Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming. Fuzzy Sets Syst 119(1):129–138
Zurück zum Zitat Shashikhin VN (2001) Solution of an interval matrix game in mixed strategies. Izv Akad Nauk Teor Sist Upr 5:97–104MathSciNet Shashikhin VN (2001) Solution of an interval matrix game in mixed strategies. Izv Akad Nauk Teor Sist Upr 5:97–104MathSciNet
Zurück zum Zitat Thomas LC (2003) Games, theory and applications. Dover Publications Inc., Mineola, NY, reprint of the 1986 edition Thomas LC (2003) Games, theory and applications. Dover Publications Inc., Mineola, NY, reprint of the 1986 edition
Zurück zum Zitat von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, PrincetonMATH von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, PrincetonMATH
Metadaten
Titel
Brown–Robinson method for interval matrix games
verfasst von
Emrah Akyar
Handan Akyar
Serkan Ali Düzce
Publikationsdatum
01.10.2011
Verlag
Springer-Verlag
Erschienen in
Soft Computing / Ausgabe 10/2011
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-011-0703-6

Weitere Artikel der Ausgabe 10/2011

Soft Computing 10/2011 Zur Ausgabe