Araştırma Makalesi
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A New Game Value Approach for Infinite Interval Matrix Games

Yıl 2021, Cilt: 25 Sayı: 6, 1343 - 1351, 31.12.2021

Aykut Or Gönül Selin Savaşkan

https://doi.org/10.16984/saufenbilder.991897

Öz

The purpose of this paper is to determine when and under which conditions the solution and game value of the infinite interval matrix games will exist. Firstly, the concept of a reasonable solution defined in interval matrix games was extended to infinite interval matrix games. Then, the solution and game value were characterized by using sequences of interval numbers (defined by Chiao, 2002) and their concept of convergence of interval numbers. Considering that each row or column of the payoff matrix is a sequence of interval numbers, we assume that each row converges to the same interval number α ̃=[α_l,α_r] and each column to the same interval number β ̃=[β_l,β_r]. In a conclusion, the existence of the solution of G ̃ is shown.

Anahtar Kelimeler

infinite matrix games interval matrix games reasonable solution

Destekleyen Kurum

Çanakkale Onsekiz Mart University

Proje Numarası

FBA-2019-2807

Teşekkür

We would like to thank the reviewers, editors, and Canakkale Onsekiz Mart University Scientific Research Projects Coordination Unit who supported the work.

Kaynakça

  • [1] E. N. Barron, Game Theory an Introduction, John Wiley & Sons Inc., New Jersey, 1-108, 2008.
  • [2] A. Cegielski, “Approximation of some zero-sum noncontinuous games by a matrix game”, Comment. Math., 2261-267, 1991.
  • [3] K.P. Chiao, “Fundamental Properties of Interval Vector Max-Norm”, Tamsui Oxf J Math Sci, 18(2):219-233, 2002.
  • [4] D.W. Collins and C. Hu, “Studying interval valued matrix games with fuzzy logic” Soft Comput, 12(2):147-155, 2008.
  • [5] H. Ishibuchi and H. Tanaka, “Multi-objective Programming in Optimization of the Interval Objective Function”, European Journal of Operational Research, 48: 219-225, 1990.
  • [6] D.F. Li, J.X. Nan and M.J. Zhang, “Interval programming models for matrix games with interval payoffs”, Optimization Methods and Software, 27(1), 1-16, 2012.
  • [7] E. Marchi, “On the minimax theorem of the theory of games”, Ann. Mat. Pura Appl. 77, 207-282, 1967.
  • [8] R.E. Moore, Method and Application of Interval Analysis, SIAM, Philadelphia, 1979.
  • [9] L.M. Naya, “Zero-sum continuous games with no compact support”, International J. Game Theory, 25(1), 93-111, 1996.
  • [10] L.M. Naya, “Weak topology and infinite matrix games”, Int J Game Theory, 27, pp:219-229, 1998.
  • [11] L.M. Naya, “On the Value of Some Infinite Matrix Games”, Mathematics of Operation Research, 26(1): 82-88, 2001.
  • [12] P.K. Nayak and T.K. Pal, “Linear Programming Technique To Solve Two-Person Matrix Games With Interval Payoffs”, Asia Pacific J of Operation Research, 26(2), 285-305, 2009.
  • [13] V.J Neuman and O. Morgenstern, “Theory of Games and Economic Behavior”, New York, Science Editions, John Wiley and Sons, Inc. third edition, 85-165, 1944.
  • [14] G., Owen, Game Theory, Third Edition Academic Press, 1995.
  • [15] A. Sengupta and T.K. Pal, “A-index for ordering interval numbers”, Presented in Indian Science Congress. Delhi University, January 3-8, 1997.
  • [16] A. Sengupta and T.K. Pal, “On comparing interval numbers”, European Journal of Operational Research, 27: 28-43, 2000.
  • [17] A. 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, 119: 129-138, 2001.
  • [18] A. Sengupta and T.K. Pal, “Fuzzy Preference Ordering of Interval Numbers in Decision Problems”, Studies in Fuzziness and Soft Computing 238, Springer, Berlin, 2009.
  • [19] S.H Tijs, “Semi Infinite and infinite matrix and bimatrix games”, Ph.D. thesis, University of Nijmegan, 1975.

Yıl 2021, Cilt: 25 Sayı: 6, 1343 - 1351, 31.12.2021

Aykut Or Gönül Selin Savaşkan

https://doi.org/10.16984/saufenbilder.991897

Öz

Proje Numarası

FBA-2019-2807

Kaynakça

  • [1] E. N. Barron, Game Theory an Introduction, John Wiley & Sons Inc., New Jersey, 1-108, 2008.
  • [2] A. Cegielski, “Approximation of some zero-sum noncontinuous games by a matrix game”, Comment. Math., 2261-267, 1991.
  • [3] K.P. Chiao, “Fundamental Properties of Interval Vector Max-Norm”, Tamsui Oxf J Math Sci, 18(2):219-233, 2002.
  • [4] D.W. Collins and C. Hu, “Studying interval valued matrix games with fuzzy logic” Soft Comput, 12(2):147-155, 2008.
  • [5] H. Ishibuchi and H. Tanaka, “Multi-objective Programming in Optimization of the Interval Objective Function”, European Journal of Operational Research, 48: 219-225, 1990.
  • [6] D.F. Li, J.X. Nan and M.J. Zhang, “Interval programming models for matrix games with interval payoffs”, Optimization Methods and Software, 27(1), 1-16, 2012.
  • [7] E. Marchi, “On the minimax theorem of the theory of games”, Ann. Mat. Pura Appl. 77, 207-282, 1967.
  • [8] R.E. Moore, Method and Application of Interval Analysis, SIAM, Philadelphia, 1979.
  • [9] L.M. Naya, “Zero-sum continuous games with no compact support”, International J. Game Theory, 25(1), 93-111, 1996.
  • [10] L.M. Naya, “Weak topology and infinite matrix games”, Int J Game Theory, 27, pp:219-229, 1998.
  • [11] L.M. Naya, “On the Value of Some Infinite Matrix Games”, Mathematics of Operation Research, 26(1): 82-88, 2001.
  • [12] P.K. Nayak and T.K. Pal, “Linear Programming Technique To Solve Two-Person Matrix Games With Interval Payoffs”, Asia Pacific J of Operation Research, 26(2), 285-305, 2009.
  • [13] V.J Neuman and O. Morgenstern, “Theory of Games and Economic Behavior”, New York, Science Editions, John Wiley and Sons, Inc. third edition, 85-165, 1944.
  • [14] G., Owen, Game Theory, Third Edition Academic Press, 1995.
  • [15] A. Sengupta and T.K. Pal, “A-index for ordering interval numbers”, Presented in Indian Science Congress. Delhi University, January 3-8, 1997.
  • [16] A. Sengupta and T.K. Pal, “On comparing interval numbers”, European Journal of Operational Research, 27: 28-43, 2000.
  • [17] A. 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, 119: 129-138, 2001.
  • [18] A. Sengupta and T.K. Pal, “Fuzzy Preference Ordering of Interval Numbers in Decision Problems”, Studies in Fuzziness and Soft Computing 238, Springer, Berlin, 2009.
  • [19] S.H Tijs, “Semi Infinite and infinite matrix and bimatrix games”, Ph.D. thesis, University of Nijmegan, 1975.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Aykut Or 0000-0001-5279-0057

Gönül Selin Savaşkan 0000-0002-9978-6941

Proje Numarası FBA-2019-2807
Yayımlanma Tarihi 31 Aralık 2021
Gönderilme Tarihi 6 Eylül 2021
Kabul Tarihi 21 Ekim 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 25 Sayı: 6

Kaynak Göster

APA Or, A., & Savaşkan, G. S. (2021). A New Game Value Approach for Infinite Interval Matrix Games. Sakarya University Journal of Science, 25(6), 1343-1351. https://doi.org/10.16984/saufenbilder.991897
AMA Or A, Savaşkan GS. A New Game Value Approach for Infinite Interval Matrix Games. SAUJS. Aralık 2021;25(6):1343-1351. doi:10.16984/saufenbilder.991897
Chicago Or, Aykut, ve Gönül Selin Savaşkan. “A New Game Value Approach for Infinite Interval Matrix Games”. Sakarya University Journal of Science 25, sy. 6 (Aralık 2021): 1343-51. https://doi.org/10.16984/saufenbilder.991897.
EndNote Or A, Savaşkan GS (01 Aralık 2021) A New Game Value Approach for Infinite Interval Matrix Games. Sakarya University Journal of Science 25 6 1343–1351.
IEEE A. Or ve G. S. Savaşkan, “A New Game Value Approach for Infinite Interval Matrix Games”, SAUJS, c. 25, sy. 6, ss. 1343–1351, 2021, doi: 10.16984/saufenbilder.991897.
ISNAD Or, Aykut - Savaşkan, Gönül Selin. “A New Game Value Approach for Infinite Interval Matrix Games”. Sakarya University Journal of Science 25/6 (Aralık 2021), 1343-1351. https://doi.org/10.16984/saufenbilder.991897.
JAMA Or A, Savaşkan GS. A New Game Value Approach for Infinite Interval Matrix Games. SAUJS. 2021;25:1343–1351.
MLA Or, Aykut ve Gönül Selin Savaşkan. “A New Game Value Approach for Infinite Interval Matrix Games”. Sakarya University Journal of Science, c. 25, sy. 6, 2021, ss. 1343-51, doi:10.16984/saufenbilder.991897.
Vancouver Or A, Savaşkan GS. A New Game Value Approach for Infinite Interval Matrix Games. SAUJS. 2021;25(6):1343-51.
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