Yazar "İzgi, Burhaneddin" seçeneğine göre listele
Listeleniyor 1 - 7 / 7
Sayfa Başına Sonuç
Sıralama seçenekleri
Öğe A holistic matrix norm-based alternative solution method for Markov reward games(Elsevier Science Inc, 2025) İzgi, Burhaneddin; Özkaya, Murat; Üre, Nazım Kemal; Perc, MatjazIn this study, we focus on examining single-agent stochastic games, especially Markov reward games represented in the form of a decision tree. We propose an alternative solution method based on the matrix norms for these games. In contrast to the existing methods such as value iteration, policy iteration, and dynamic programming, which are state-and-action-based approaches, the proposed matrix norm-based method considers the relevant stages and their actions as a whole and solves it holistically for each stage without computing the effects of each action on each state's reward individually. The new method involves a distinct transformation of the decision tree into a payoff matrix for each stage and the utilization of the matrix norm of the obtained payoff matrix. Additionally, the concept of the moving matrix is integrated into the proposed method to incorporate the impacts of all actions on the stage simultaneously, rendering the method holistic. Moreover, we present an explanatory algorithm for the implementation of the method and also provide a comprehensive solution diagram explaining the method figuratively. As a result, we offer a new and alternative perspective for solving the games with the help of the proposed method due to the simplicity of utilization of the matrix norms in addition to the existing methods. For clarification of the matrix norm-based method, we demonstrate the figurative application of the method on a benchmark Markov reward game with 2-stages and 2-actions and a comprehensive implementation of the method on a game consisting of 3-stages and 3-actions.Öğe Effects of the quarantine on the individuals' risk of Covid-19 infection: Game theoretical approach(Elsevier B.V., 2021) Özkaya, Murat; İzgi, BurhaneddinIn this study, we analyze the general or self-quarantine effects to the spread of the first wave of Covid-19 pandemic in the view of the game-theoretical approach. As in some other applications of game theory in different aspects of the literature, we focus on only the application of game theory to present the effects of quarantine during the three different stages -the start, the spread, the end- of the pandemic. We first choose three countries such as South Korea for self-quarantine, Italy, and Turkey for general quarantine during the analysis of the different stages of the spread. Then, we present a formula that will be an important tool for the creation of the payoff matrices and give the general procedure for the creation of the payoff matrix for each stage of the pandemic process. After that, we generate the payoff bimatrix for each stage of the pandemic by using the average of the daily diagnosis number/number of tests for each country. Moreover, we try to find the optimal strategy of the game. Additionally, to determine the necessity of the continuity of the quarantine, we use the repeated game approach in our analysis, as well. Therefore, we convert the game only for the spread stage to the repeated game for each country. Finally, we obtain the Nash equilibrium of all games for each level of the pandemic. The results show that the quarantine has important effects to be infected or not, and the spread of the pandemic at each level. In addition to these analysis results, we compare the death rates of the considered countries and show that the results are almost parallel to that are obtained for the quarantine requirement of each country by game-theoretical approaches.Öğe Machine learning driven extended matrix norm method for the solution of large-scale zero-sum matrix games(Elsevier B.V., 2023) İzgi, Burhaneddin; Özkaya, Murat; Üre, Nazım Kemal; Perc, MatjažIn this paper, we develop a novel machine learning-driven framework for solving large-scale zero-sum matrix games by exploiting patterns discovered from the offline extended matrix norm method. Modern game theoretic tools such as the extended matrix norm method allow rapid estimation of the game values for small-scale zero-sum games by computing norms of the payoff matrix. However, as the number of strategies in the game increases, obtaining an accurate value estimation through the extended matrix norm method becomes more difficult. In this work, we propose a novel neural network architecture for large-scale zero-sum matrix games, which takes the estimations of the extended matrix norm method and payoff matrix as inputs, and provides a rapid estimation of the game value as the output. The proposed architecture is trained over various random zero-sum games of different dimensions. Results show that the developed framework can obtain accurate value predictions, with a less than 10% absolute relative error, for games with up to 50 strategies. Also of note, after the network is trained, solution predictions can be obtained in real-time, which makes the proposed method particularly useful for real-world applications.Öğe Matrix norm based hybrid Shapley and iterative methods for the solution of stochastic matrix games(Elsevier Science Inc, 2024) İzgi, Burhaneddin; Özkaya, Murat; Üre, Nazım Kemal; Perc, MatjazIn this paper, we present four alternative solution methods to Shapley iteration for the solution of stochastic matrix games. We first combine the extended matrix norm method for stochastic matrix games with Shapley iteration and then state and prove the weak and strong hybrid versions of Shapley iterations. Then, we present the semi-extended matrix norm and iterative semi-extended matrix norm methods, which are analytic-solution-free methods, for finding the approximate solution of stochastic matrix games without determining the strategy sets. We illustrate comparisons between the Shapley iteration, weak and strong hybrid Shapley iterations, semi-extended matrix norm method, and iterative semi-extended matrix norm method with several examples. The results reveal that the strong and weak hybrid Shapley iterations improve the Shapley iteration and decrease the number of iterations, and the strong hybrid Shapley iteration outperforms all the other proposed methods. Finally, we compare these methods and present their performance analyses for large-scale stochastic matrix games as well.Öğe Matrix norm methods for zero-sum fuzzy matrix games with payoffs of triangular fuzzy numbers(Elsevier Science Inc, 2024) İzgi, Burhaneddin; Köçken, Hale Gonce; Özkaya, MuratIn this paper, we mainly consider the solution of two -person zero -sum fuzzy matrix games with payoffs of triangular fuzzy numbers. Contrary to the literature, we focus on developing the methods to solve the game directly based on only the norms of the payoff matrix holistically, without solving a linear programming problem or handling sub -games created by taking the components of fuzzy numbers separately. For this purpose, we first present fuzzy versions of 1 -norm and infinity -norm with the help of a ranking function and develop the fuzzy matrix norm method to obtain an approximate solution of the zero -sum fuzzy matrix game. In addition to this approach, we provide the fuzzy extended matrix norm method as an enhanced version of the method, which involves the use of newly defined fuzzy matrix norms. Thus, we managed to avoid the complexity of the optimization process of the linear programming problem via the proposed matrix norm -based methods. Finally, we illustrate the implementation of the methods by considering several benchmark examples and a 3 x 3 fuzzy matrix game.Öğe Oyun Teorisi Açısından Türkiye Gözünden Finlandiya ve İsveç’in NATO’ya Üyelik Süreci(2024) Özkaya, Murat; Baştan, Yücel; İzgi, BurhaneddinBu çalışmada, İsveç ve Finlandiya’nın NATO üyelik başvurularının Türkiye tarafından onaylanma sürecini belirsizlik altında 3-boyutlu (3B) karar verme kriterlerini kullanarak inceledik. İlk olarak İsveç ve Finlandiya ile Türkiye’nin ilişkisini dış politika analizlerinde öne çıkan üç ana boyut politik, ekonomik ve askeri ve her bir ana boyutun üçer alt boyutunu göz önünde bulundurarak ele aldık. Daha sonra bu ilişkilerin Türkiye açısında önem derecelerini önem derecesi ölçeği kullanarak sıraladık ve bu sıralamalara uygun temsili değerler atayarak her bir boyut için 3-boyutlu getiri matrisleri oluşturulmuştur. Son olarak, belirsizlik altında 3-boyutlu karar verme kriterleri olan 3B Laplace kriteri, 3B Wald kriteri, 3B Hurwicz kriteri ve 3B Savage kriteri ile analizleri yaptık. 3Bkarar verme kriterlerinin kullanılmasının en büyük avantajı İsveç ve Finlandiya’nın politik, ekonomik ve askeri etkilerinin karar süreci üzerindeki etkilerini eş zamanlı incelemeye imkan vermesidir. Bu açıdan, bu çalışma belirsizlik altında 3B karar verme kriterlerinin uygulamasının yapıldığı ilk çalışma olması nedeniyle önem taşımaktadır. Game theory; 3D decision criteria; 3D matrices; International relations; International security; NATOÖğe Uluslararası Bir Krizin Oyun Teorisi ile Matematiksel Olarak Modellenmesi(2021) Özkaya, Murat; İzgi, BurhaneddinBu 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.
