Research Article
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Peer Group Situations and Modeling with Game Theory

Year 2024, , 194 - 206, 18.07.2024
https://doi.org/10.56554/jtom.1292921

Abstract

Peer group situations and related games appear in various economic and operations research problems. For example, a restricted class of cooperative games that emerge when studying coalitional behavior in tenders is expressed by peer group games. In peer group situations, the social configuration of organizations influences the potential possibilities of all representative groups. Each representative given in a strict hierarchy has a relationship with the leader, either directly or indirectly, with the help of one or more representatives. The economic possibility of a representative is constrained by his position in the hierarchy. The group leader, which is important for the representative in the peer group, emerges as the group formed by all middle-level representatives in the hierarchy given between the representative himself and the leader. Such a group of representatives is called a peer group. In this study, peer group situations and related peer group games are discussed. The aim of the study is to show that peer group games can be used in different economic situations such as tender situations, ranking situations and airport situations in our real life. In addition, in this study, economic and operations research situations related to peer group games will be discussed.

Project Number

The paper comes from the SEMIT 2022 September Conference

References

  • Alparslan Gök, S.Z., Palancı, O., Yücesan, Z., (2018). Handbook of Research on Emergent Applications of Optimization Algorithms, IGI Global. Doi: https://doi.org/10.4018/978-1-5225-2990-3
  • Banzhaf, J.F., (1965). Weighted Voting Doesn.t Work: A Mathematical Analysis. Rutgers University Law Review, 19, 317-343. Erişim adresi: https://link.springer.com/article/10.1007/BF01194250
  • Branzei, R., Dimitrov, D., Tijs, S., (2008). Models in Cooperative Game Theory. Springer-Verlag, 204p, Berlin. Erişim adresi: https://research.tilburguniversity.edu/en/publications/models-in-cooperative-game-theory-2
  • Brânzei, R., Fragnelli, V., Tijs, S. (2002). Tree-connected peer group situations and peer group games. Mathematical Methods of Operations Research, 55, 93-106. Doi: https://doi.org/10.1007/s001860200176
  • Branzei, R., Mallozzi, L., Tijs, S., (2010). Peer Group Situations and Games with Interval Uncertainty. International Journal of Mathematics, Game Theory, and Algebra, 19(5-6), 381–388. Erişim adresi: https://www.iris.unina.it/handle/11588/599668
  • Branzei, R., Tijs, S., Alparslan Gök, S.Z., (2010.) How to handle interval solutions for cooperative interval games. International Journal of Uncertainty,Fuzziness and Knowledge-Based Systems, 18(2); 123. https://doi.org/10.1142/S0218488510006441
  • Curiel, I. (1997). Cooperative Game Theory and Applications. Springer-Verlag, 194p, USA. Erişim adresi: https://books.google.com.tr
  • Curiel, I., Pederzoli, G., Tijs, S., (1989). Sequencing games. Eur. J. Op. Res., (40), 344. Erişim adresi: https://pure.uvt.nl/ws/portalfiles/portal/659469/27020_12973.
  • Deng, X., Papadimitriou, C. H. (1994). On the complexity of cooperative solution concepts. Mathematics of operations research, 19(2), 257-266. doi: https://doi.org/10.1287/moor.19.2.25
  • Driessen, T.S.H., Funaki, Y., (1991). Coincidence of and collinearity between game-theoretic solutions. OR Spectrum, 13(1), 15-30. Erişim adresi: https://link.springer.com/article/10.1007/BF01719767
  • Gilles, R. P., Owen, G., van den Brink, R. (1992). Games with permission structures: the conjunctive approach. International Journal of Game Theory, 20(3), 277-293. doi: https://doi.org/10.1007/BF01253782
  • Littlechild, S. C., Owen, G. (1976). A further note on the nucleoous of the “airport game”. International Journal of Game Theory, 5, 91-95. Erişim adresi: https://link.springer.com/article/10.1007/BF01753311
  • Myerson, R. B. (1977). Graphs and cooperation in games. Mathematics of operations research, 2(3), 225-229. https://doi.org/10.1287/moor.2.3.225 Owen, G. (1986). Values of graph-restricted games. SIAM Journal on Algebraic Discrete Methods, 7(2), 210-220. doi: https://doi.org/10.1137/0607025
  • Rasmusen, E. (1989). Games and information. An introduction to game theory. Blackwell, Oxford UK & Cambridge USA. Erişim adresi: http://ndl.ethernet.edu.et/bitstream/123456789/48245/1/12.pdf
  • Shapley, L. S. (1953). А Value for n-Person Games: Annals of Math. Studies, (28), 307-317. Erişim adresi: https://www.rand.org/content/dam/rand/pubs/papers/2021/P295.pdf
  • Smith, W. E. (1956). Various optimizers for single-stage production, Naval Res. Logist. Quart. (3), 59-66. Erişim adresi: https://books.google.com.tr
  • Tijs, S. (2003). Introduction to game theory. Springer. Hindustan Book Agency, India. Erişim adresi: https://eclass.unipi.gr/modules/document/file.php/DES101/Βιβλίο%20μαθήματος%20%28Αγγλική%20δωρεάν %20έκδοση%29/%40An%20Introduction
  • von Neumann, J., Morgenstern, O., (1947). Theory of Games and Economic Behavior. Princeton University Press, 776p, Princeton. Erişim adresi: https://psycnet.apa.org/record/1947-03159-000
  • Yücesan, Z. (2017). Akran grup oyunlarının gri sistem teorisi ile modellenmesi (Master's thesis, Fen Bilimleri Enstitüsü), Süleyman Demirel Üniversitesi. Isparta. Erişim adresi: https://acikbilim.yok.gov.tr/handle/20.500.12812/276987

Akran Grup Durumları ve Oyun Teorisi ile Modellenmesi Üzerine

Year 2024, , 194 - 206, 18.07.2024
https://doi.org/10.56554/jtom.1292921

Abstract

Akran grup durumları ve buna bağlı kurulan oyunlar çeşitli ekonomik ve yöneylem araştırması problemlerinde karşımıza çıkmaktadır. Örneğin ihalelerde koalisyonel davranış çalışıldığı zaman ortaya çıkan kooperatif oyunların bir kısıtlanmış sınıfı akran grup oyunları ile ifade edilmektedir. Akran grup durumlarında, organizasyonların sosyal yapılandırması, tüm temsilci grupların potansiyel olasılıklarını etkilemektedir. Katı bir hiyerarşide verilen her bir temsilci bir ya da daha çok temsilcinin yardımıyla doğrudan veya dolaylı olarak lider ile ilişkilidir. Bir temsilciye ait olan ekonomik olasılık hiyerarşi içerisindeki konumu ile kısıtlanmaktadır. Akran grubundaki temsilci için önemli olan grup lideri temsilcinin kendisi ve lideri arasında verilen hiyerarşide var olan tüm orta düzeydeki temsilcilerin oluşturduğu grup olarak karşımıza çıkmaktadır. Temsilcilerin böyle bir grubu akran grup olarak adlandırılmaktadır. Bu çalışmada akran grup durumları ve ona bağlı kurulan akran grup oyunları ele alınmıştır. Çalışmanın amacı akran grup oyunlarının gerçek yaşamımızda ihale durumları, sıralama durumları ve havaalanı durumları gibi farklı ekonomik durumlarda kullanılabilir olduğunu göstermektir. Ayrıca bu çalışmada akran grup oyunları ile ilişkili ekonomik ve yöneylem araştırması durumlarına değinilecektir.

Project Number

The paper comes from the SEMIT 2022 September Conference

References

  • Alparslan Gök, S.Z., Palancı, O., Yücesan, Z., (2018). Handbook of Research on Emergent Applications of Optimization Algorithms, IGI Global. Doi: https://doi.org/10.4018/978-1-5225-2990-3
  • Banzhaf, J.F., (1965). Weighted Voting Doesn.t Work: A Mathematical Analysis. Rutgers University Law Review, 19, 317-343. Erişim adresi: https://link.springer.com/article/10.1007/BF01194250
  • Branzei, R., Dimitrov, D., Tijs, S., (2008). Models in Cooperative Game Theory. Springer-Verlag, 204p, Berlin. Erişim adresi: https://research.tilburguniversity.edu/en/publications/models-in-cooperative-game-theory-2
  • Brânzei, R., Fragnelli, V., Tijs, S. (2002). Tree-connected peer group situations and peer group games. Mathematical Methods of Operations Research, 55, 93-106. Doi: https://doi.org/10.1007/s001860200176
  • Branzei, R., Mallozzi, L., Tijs, S., (2010). Peer Group Situations and Games with Interval Uncertainty. International Journal of Mathematics, Game Theory, and Algebra, 19(5-6), 381–388. Erişim adresi: https://www.iris.unina.it/handle/11588/599668
  • Branzei, R., Tijs, S., Alparslan Gök, S.Z., (2010.) How to handle interval solutions for cooperative interval games. International Journal of Uncertainty,Fuzziness and Knowledge-Based Systems, 18(2); 123. https://doi.org/10.1142/S0218488510006441
  • Curiel, I. (1997). Cooperative Game Theory and Applications. Springer-Verlag, 194p, USA. Erişim adresi: https://books.google.com.tr
  • Curiel, I., Pederzoli, G., Tijs, S., (1989). Sequencing games. Eur. J. Op. Res., (40), 344. Erişim adresi: https://pure.uvt.nl/ws/portalfiles/portal/659469/27020_12973.
  • Deng, X., Papadimitriou, C. H. (1994). On the complexity of cooperative solution concepts. Mathematics of operations research, 19(2), 257-266. doi: https://doi.org/10.1287/moor.19.2.25
  • Driessen, T.S.H., Funaki, Y., (1991). Coincidence of and collinearity between game-theoretic solutions. OR Spectrum, 13(1), 15-30. Erişim adresi: https://link.springer.com/article/10.1007/BF01719767
  • Gilles, R. P., Owen, G., van den Brink, R. (1992). Games with permission structures: the conjunctive approach. International Journal of Game Theory, 20(3), 277-293. doi: https://doi.org/10.1007/BF01253782
  • Littlechild, S. C., Owen, G. (1976). A further note on the nucleoous of the “airport game”. International Journal of Game Theory, 5, 91-95. Erişim adresi: https://link.springer.com/article/10.1007/BF01753311
  • Myerson, R. B. (1977). Graphs and cooperation in games. Mathematics of operations research, 2(3), 225-229. https://doi.org/10.1287/moor.2.3.225 Owen, G. (1986). Values of graph-restricted games. SIAM Journal on Algebraic Discrete Methods, 7(2), 210-220. doi: https://doi.org/10.1137/0607025
  • Rasmusen, E. (1989). Games and information. An introduction to game theory. Blackwell, Oxford UK & Cambridge USA. Erişim adresi: http://ndl.ethernet.edu.et/bitstream/123456789/48245/1/12.pdf
  • Shapley, L. S. (1953). А Value for n-Person Games: Annals of Math. Studies, (28), 307-317. Erişim adresi: https://www.rand.org/content/dam/rand/pubs/papers/2021/P295.pdf
  • Smith, W. E. (1956). Various optimizers for single-stage production, Naval Res. Logist. Quart. (3), 59-66. Erişim adresi: https://books.google.com.tr
  • Tijs, S. (2003). Introduction to game theory. Springer. Hindustan Book Agency, India. Erişim adresi: https://eclass.unipi.gr/modules/document/file.php/DES101/Βιβλίο%20μαθήματος%20%28Αγγλική%20δωρεάν %20έκδοση%29/%40An%20Introduction
  • von Neumann, J., Morgenstern, O., (1947). Theory of Games and Economic Behavior. Princeton University Press, 776p, Princeton. Erişim adresi: https://psycnet.apa.org/record/1947-03159-000
  • Yücesan, Z. (2017). Akran grup oyunlarının gri sistem teorisi ile modellenmesi (Master's thesis, Fen Bilimleri Enstitüsü), Süleyman Demirel Üniversitesi. Isparta. Erişim adresi: https://acikbilim.yok.gov.tr/handle/20.500.12812/276987
There are 19 citations in total.

Details

Primary Language Turkish
Subjects Applied Mathematics
Journal Section Research Article
Authors

Medine Demir 0000-0002-9543-0753

Pınar Usta 0000-0001-9809-3855

Sırma Zeynep Alparslan Gök 0000-0001-9435-0527

Project Number The paper comes from the SEMIT 2022 September Conference
Early Pub Date July 18, 2024
Publication Date July 18, 2024
Submission Date May 5, 2023
Acceptance Date March 20, 2024
Published in Issue Year 2024

Cite

APA Demir, M., Usta, P., & Alparslan Gök, S. Z. (2024). Akran Grup Durumları ve Oyun Teorisi ile Modellenmesi Üzerine. Journal of Turkish Operations Management, 8(1), 194-206. https://doi.org/10.56554/jtom.1292921
AMA Demir M, Usta P, Alparslan Gök SZ. Akran Grup Durumları ve Oyun Teorisi ile Modellenmesi Üzerine. JTOM. July 2024;8(1):194-206. doi:10.56554/jtom.1292921
Chicago Demir, Medine, Pınar Usta, and Sırma Zeynep Alparslan Gök. “Akran Grup Durumları Ve Oyun Teorisi Ile Modellenmesi Üzerine”. Journal of Turkish Operations Management 8, no. 1 (July 2024): 194-206. https://doi.org/10.56554/jtom.1292921.
EndNote Demir M, Usta P, Alparslan Gök SZ (July 1, 2024) Akran Grup Durumları ve Oyun Teorisi ile Modellenmesi Üzerine. Journal of Turkish Operations Management 8 1 194–206.
IEEE M. Demir, P. Usta, and S. Z. Alparslan Gök, “Akran Grup Durumları ve Oyun Teorisi ile Modellenmesi Üzerine”, JTOM, vol. 8, no. 1, pp. 194–206, 2024, doi: 10.56554/jtom.1292921.
ISNAD Demir, Medine et al. “Akran Grup Durumları Ve Oyun Teorisi Ile Modellenmesi Üzerine”. Journal of Turkish Operations Management 8/1 (July 2024), 194-206. https://doi.org/10.56554/jtom.1292921.
JAMA Demir M, Usta P, Alparslan Gök SZ. Akran Grup Durumları ve Oyun Teorisi ile Modellenmesi Üzerine. JTOM. 2024;8:194–206.
MLA Demir, Medine et al. “Akran Grup Durumları Ve Oyun Teorisi Ile Modellenmesi Üzerine”. Journal of Turkish Operations Management, vol. 8, no. 1, 2024, pp. 194-06, doi:10.56554/jtom.1292921.
Vancouver Demir M, Usta P, Alparslan Gök SZ. Akran Grup Durumları ve Oyun Teorisi ile Modellenmesi Üzerine. JTOM. 2024;8(1):194-206.

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