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Uluslararası Bir Krizin Oyun Teorisi ile Matematiksel Olarak Modellenmesi

Year 2021, Volume: 10 Issue: 4, 1334 - 1341, 31.12.2021
https://doi.org/10.17798/bitlisfen.942655

Abstract

Bu çalışmamızda, herhangi iki ülke arasında yaşanan karşılıklı can ve mal kayıplarıyla devam eden uluslararası bir krizi oyun teorisi kullanarak modelledik. İlk olarak, inceleyeceğimiz problemi geçmişte yaşanan bazı gerçek krizleri inceleyerek detaylarıyla tanımladık. Daha sonra, detaylı bir şekilde tanımladığımız bu problemi oyun teorisinin en bilinen oyunlarından biri olan tutuklu ikilemini temel alarak modelledik. İlk olarak, modellediğimiz bu oyunun saf Nash denge noktasını bulduk. Buna ek olarak, oyuncuların yani ülkelerin tekrar krize sürüklenmesi durumunda ne yapması gerektiğini incelemek için oyunu tekrarlı oyun haline getirdik. Daha sonra bu oyundaki stratejileri ve sonuçları açıkça görebilmek için oyunumuzu oyun ağacı şeklinde ifade ettik. Ardından, oluşan bu yeni durum için yeni oyunun getiri matrisini oluşturduk. Son olarak tekrarlı oyun haline gelen oyunun saf Nash denge noktalarını bulduk. Ayrıca, ikinci oyunun bir alt oyununu kullanarak oyunumuz farklı bir açıdan tekrar çözdük. Böylece uluslararası bir krizi tutuklu ikilemini kullanarak başarıyla modelledik ve sonuçlarını sunduk.

References

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  • Guseinov, K. G., Akyar, E., Düzce S. A., 2010, Oyun Teorisi: Çatışma ve Anlaşmanın Matematiksel Modelleri, Seçkin.
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  • Von Neumann, J., Morgenstern, O., 1944, Theory of Games and Economic Behaviour, Princeton University Press.
  • Snidal, D., 1985, The game theory of international politics. World Politics, Vol.38, No.1, p.25-55.
  • P. Allan, P., Dupont, C., 1999, International Relation Theory and Game Theory: Baroque Modeling Choices and Empirical Robustness, International Political Science Review, 20(1), p.23-47.
  • Correa, H., 2001, Game theory as an instrument for the analysis of international relations. Ritsumaikan International Research, 14(2001), 197-208.
  • Sandler, T.ve M. Arce, D.G, 2003, Terrorism & game theory, Simulation & Gaming, Vol.34, No.3, 319-337.
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  • Aydın, S.,2009, The super power versus a regional power: A game theoretical approach to the current nuclear tension between the US and Iran, M.Sc. Thesis, The Institute of Economic and Social Sciences, Bilkent University, Ankara, pg.103.
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  • Diesen, G. 2015, EU and NATO relations with Russia: After the collapse of the Soviet Union, Routledge.
  • Bhuivan, B.A., 2016, An overview of game theory and some applications, Philosophy and Progress, Vols. LIX-LX, p. 112-128.
  • S. Rass, S. König, ve S. Schauer, Defending against advanced persistent threats using game theory. PLOS ONE, 12(1), e0168657, 2017.
  • Levi,N., 2017, Applying game theory to North Korea-China relations, Journal of Modern Science, 33(2), 355-366.
  • Yin, J.Z. ve Hamilton, M.H., 2018, The conundrum of US-China trade relations through game theory modelling. Journal of Applied Business and Economic, Vol.20(8)2018, 133-150.
  • Tavares, J.M. ve Tran, X., 2019, Is there a strategic independence between the USA and Canada in the tourism sector? An analysis using game theory. Tourism Planning Development,13:3,304-317.
  • Özdemir, Ö., 2019, An Application of Expected Utility Modeling and Game Theory in IR: Assessment of International Bargaining on Iran’s Nuclear Program, All Azimuth, V8, N2, 205-30.
  • Wen, Y., Li, H., Du, X., Yang, K., Casazza, M., Liu, G., 2019. Analytical approach to win-win game analysis for Chinese and Japanese development assistance strategies in Africa. Ecological Indicators, 96(2019), 219-229.
  • Gassama,S.K., Ebrahimi, M., Yusoff, B.K., 2020. The oil hegemonic system and game theory: Regional versus trans-regional Powers in the Middle East. Contemproary Review of the Middle East, 7(3), 358-376.
  • Krapohl, S., Ocelik, V., Walentek, D.M., 2020. The instability of globalization: Applying evolutionary game theory to global trade cooperation. Public Choice (2020).
  • Ferguson, T.S., 2014. Game Theory Part II, Mathematics Depart¬ment UCLA, 2nd Edition.
  • Ferguson, T.S., 2014. Game Theory Part III, Mathematics Depart¬ment UCLA, 2nd Edition.
  • Prisner, E., G., 2014, Game Theory through Examples, The Mathematical Association of America.
  • Mazalov, V., 2014, Mathematical Game Theory and Applications, John Wiley & Sons.
  • Baron, E. N., 2013, Game Theory: An Introduction, John Wiley & Sons.
Year 2021, Volume: 10 Issue: 4, 1334 - 1341, 31.12.2021
https://doi.org/10.17798/bitlisfen.942655

Abstract

References

  • Shubik, M.,1964, Game Theory and Related Approaches to Social Behaviour: Selections, John Wiley & Sons.
  • Guseinov, K. G., Akyar, E., Düzce S. A., 2010, Oyun Teorisi: Çatışma ve Anlaşmanın Matematiksel Modelleri, Seçkin.
  • Haywood, Jr, O. G., 1954, Military decision and game theory, Journal of the Operation Research Society of America, Vol.2, No.4.
  • Von Neumann, J., Morgenstern, O., 1944, Theory of Games and Economic Behaviour, Princeton University Press.
  • Snidal, D., 1985, The game theory of international politics. World Politics, Vol.38, No.1, p.25-55.
  • P. Allan, P., Dupont, C., 1999, International Relation Theory and Game Theory: Baroque Modeling Choices and Empirical Robustness, International Political Science Review, 20(1), p.23-47.
  • Correa, H., 2001, Game theory as an instrument for the analysis of international relations. Ritsumaikan International Research, 14(2001), 197-208.
  • Sandler, T.ve M. Arce, D.G, 2003, Terrorism & game theory, Simulation & Gaming, Vol.34, No.3, 319-337.
  • Wishnietsky, A., 2007, Applying game theory to presidental mistakes, Ph.D. Thesis, Graduate Faculty of Auburn University, Auburn, Alabama, pg.188.
  • Aydın, S.,2009, The super power versus a regional power: A game theoretical approach to the current nuclear tension between the US and Iran, M.Sc. Thesis, The Institute of Economic and Social Sciences, Bilkent University, Ankara, pg.103.
  • Ferreira, F. A., Ferreira, F. 2010, Simultaneous decisions or leadership in an international competition, AIP Conference Proceedings, Vol.1281, 2010, 804-807
  • Omrani, H., Beiragh, G.R., ve Kaleibari, S.S.,2015, Performance assessment of Iranian electricity distribution companies by an integrated cooperative game data envelopment anaylsis principal component analysis approach, Electrical Powern and Energy Systems,64(2015), 617-625.
  • Diesen, G. 2015, EU and NATO relations with Russia: After the collapse of the Soviet Union, Routledge.
  • Bhuivan, B.A., 2016, An overview of game theory and some applications, Philosophy and Progress, Vols. LIX-LX, p. 112-128.
  • S. Rass, S. König, ve S. Schauer, Defending against advanced persistent threats using game theory. PLOS ONE, 12(1), e0168657, 2017.
  • Levi,N., 2017, Applying game theory to North Korea-China relations, Journal of Modern Science, 33(2), 355-366.
  • Yin, J.Z. ve Hamilton, M.H., 2018, The conundrum of US-China trade relations through game theory modelling. Journal of Applied Business and Economic, Vol.20(8)2018, 133-150.
  • Tavares, J.M. ve Tran, X., 2019, Is there a strategic independence between the USA and Canada in the tourism sector? An analysis using game theory. Tourism Planning Development,13:3,304-317.
  • Özdemir, Ö., 2019, An Application of Expected Utility Modeling and Game Theory in IR: Assessment of International Bargaining on Iran’s Nuclear Program, All Azimuth, V8, N2, 205-30.
  • Wen, Y., Li, H., Du, X., Yang, K., Casazza, M., Liu, G., 2019. Analytical approach to win-win game analysis for Chinese and Japanese development assistance strategies in Africa. Ecological Indicators, 96(2019), 219-229.
  • Gassama,S.K., Ebrahimi, M., Yusoff, B.K., 2020. The oil hegemonic system and game theory: Regional versus trans-regional Powers in the Middle East. Contemproary Review of the Middle East, 7(3), 358-376.
  • Krapohl, S., Ocelik, V., Walentek, D.M., 2020. The instability of globalization: Applying evolutionary game theory to global trade cooperation. Public Choice (2020).
  • Ferguson, T.S., 2014. Game Theory Part II, Mathematics Depart¬ment UCLA, 2nd Edition.
  • Ferguson, T.S., 2014. Game Theory Part III, Mathematics Depart¬ment UCLA, 2nd Edition.
  • Prisner, E., G., 2014, Game Theory through Examples, The Mathematical Association of America.
  • Mazalov, V., 2014, Mathematical Game Theory and Applications, John Wiley & Sons.
  • Baron, E. N., 2013, Game Theory: An Introduction, John Wiley & Sons.
There are 27 citations in total.

Details

Primary Language Turkish
Journal Section Araştırma Makalesi
Authors

Murat Özkaya 0000-0001-7241-4710

Burhaneddin İzgi 0000-0002-8441-9137

Publication Date December 31, 2021
Submission Date May 25, 2021
Acceptance Date November 16, 2021
Published in Issue Year 2021 Volume: 10 Issue: 4

Cite

IEEE M. Özkaya and B. İzgi, “Uluslararası Bir Krizin Oyun Teorisi ile Matematiksel Olarak Modellenmesi”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 10, no. 4, pp. 1334–1341, 2021, doi: 10.17798/bitlisfen.942655.

Bitlis Eren University
Journal of Science Editor
Bitlis Eren University Graduate Institute
Bes Minare Mah. Ahmet Eren Bulvari, Merkez Kampus, 13000 BITLIS