Uluslararası Bir Krizin Oyun Teorisi ile Matematiksel Olarak Modellenmesi

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.

Mathematical Modeling of an International Crisis with Game Theory

In this study, we discuss a crisis occurring between any two countries and continuing with reciprocity losses of life and property in terms of game theory. First of all, we describe the problem in detail taking account of the real crisis that has occurred in the near-past. We then model the problem which is identified on the basis of The Prisoner’s dilemma, which is one of the well-known game in game theory. We find the pure Nash equilibrium point of the first game. Later on, we model the game under the fact that these players have a crisis again, that is, we construct a repeated game. We expressed our game as a game tree so that we can clearly see the strategies and results in this game. Then, we created the payoff matrix of the new game for this new situation Finally we find the pure Nash equilibrium points of the new game. In addition, we solve our game again from a different perspective using a subgame of the second game. Hence, we successfully model an international crisis using the prisoner’s dilemma and present its results.

___

  • [1] Shubik M. 1964. Game Theory and Related Approaches to Social Behaviour: Selections. John Wiley & Sons. New York, USA.
  • [2] Guseinov K. G., Akyar E., Düzce S. A. 2010. Oyun Teorisi: Çatışma ve Anlaşmanın Matematiksel Modelleri. Seçkin. Ankara, Türkiye.
  • [3] Haywood Jr, O. G. 1954. Military decision and game theory. Journal of the Operation Research Society of America. 2 (4): 365-462.
  • [4] Von Neumann J., Morgenstern O. 1944. Theory of Games and Economic Behaviour. Princeton University Press. Princeton, New Jersey, USA.
  • [5] İzgi B., Özkaya M. 2019. A new perspective to the solution and creation of zero sum matrix game with matrix norms. Applied Mathematics and Computation, 341, 148-159.
  • [6] İzgi B., Özkaya M. 2019. Matris normları ile bir matris oyununun adilliğinin gösterilmesi. International Journal of Advances in Engineering and Pure Sciences, 31 (2): 126-132.
  • [7] İzgi B., Özkaya M. 2020. Tarım sigortası gerekliliğinin oyun teorisi yardımıyla gösterilmesi: Matris Norm Yaklaşımı. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi , 20 (5): 824-831.
  • [8] Özkaya M., İzgi B. 2021. Effects of the quarantine on the individuals’ risk of Covid-19 infection: Game theoretical approach, Alexandria Engineering Journal, 60 (4): 4157-4165.
  • [9] Snidal D. 1985. The game theory of international politics. World Politics, 38 (1): 25-55.
  • [10] Allan P., Dupont C. 1999. International relation theory and game theory: baroque modeling choices and empirical robustness. International Political Science Review, 20 (1): 23-47.
  • [11] Correa H. 2001. Game theory as an instrument for the analysis of international relations. Ritsumaikan International Research, 14 (2001): 197-208.
  • [12] Sandler T., M. Arce, D.G. 2003. Terrorism & game theory. Simulation & Gaming, 34 (3): 319- 337.
  • [13] Wishnietsky A. 2007, Applying Game Theory to Presidental Mistakes. Ph.D. Thesis. Graduate Faculty of Auburn University, Auburn, Alabama, 188.
  • [14] 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, 103.
  • [15] Ferreira F. A., Ferreira F. 2010. Simultaneous Decisions or Leadership in an International Competition. AIP Conference Proceedings. 1281 (2010): 804-807.
  • [16] Omrani H., Beiragh G.R., Kaleibari S.S. 2015. Performance assessment of Iranian electricity distribution companies by an integrated cooperative game data envelopment analysis principal component analysis approach. Electrical Powern and Energy Systems. 64 (2015): 617-625.
  • [17] Diesen G. 2015. EU and NATO relations with Russia: After the collapse of the Soviet Union. Routledge.
  • [18] Bhuivan B.A. 2016. An overview of game theory and some applications. Philosophy and Progress. LIX-LX: 112-128.
  • [19] Rass S., König S., Schauer S. 2017. Defending against advanced persistent threats using game theory. PLOS ONE, 12 (1), e0168657.
  • [20] Levi N. 2017. Applying game theory to North Korea-China relations. Journal of Modern Science. 33 (2): 355-366.
  • [21] Yin J.Z., Hamilton M.H. 2018. The conundrum of US-China trade relations through game theory modeling. Journal of Applied Business and Economic, 20 (8): 133-150.
  • [22] Tavares J.M., 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.
  • [23] Özdemir Ö. 2019. An application of expected utility modeling and game theory in ır: assessment of ınternational bargaining on Iran’s nuclear program. All Azimuth, 8 (2): 205-230.
  • [24] 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.
  • [25] 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.
  • [26] Krapohl S., Ocelik V., Walentek D.M. 2020. The instability of globalization: applying evolutionary game theory to global trade cooperation. Public Choice.
  • [27] Ferguson T.S. 2014. Game Theory Part II. Mathematics Department UCLA, 2nd Edition.
  • [28] Ferguson T.S. 2014. Game Theory Part III. Mathematics Department UCLA, 2nd Edition.
  • [29] Prisner E., G. 2014. Game Theory through Examples. The Mathematical Association of America, USA.
  • [30] Mazalov V. 2014. Mathematical Game Theory and Applications. John Wiley & Sons. West Sussex, U.K.
  • [31] Baron E. N. 2013. Game Theory: An Introduction. John Wiley & Sons. Hoboken, New Jersey, USA.
  • [32] Straffin P. D. 1993. Game Theory and Strategy.The Mathematical Association of America, Washington, USA.
Bitlis Eren Üniversitesi Fen Bilimleri Dergisi-Cover
  • Yayın Aralığı: Yılda 4 Sayı
  • Başlangıç: 2012
  • Yayıncı: Bitlis Eren Üniversitesi Rektörlüğü