A new perspective to the solution and creation of zero sum matrix game with matrix norms

İzgi, Burhaneddin; Özkaya, Murat

doi:10.1016/j.amc.2018.08.013

Cited by 7 publications

(12 citation statements)

References 13 publications

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“…According to the properties of the mixed-strategy Nash equilibrium in [28], inequality (9) can be formulated by the following expression, and the corresponding optimal solution of formulation (10) is the mixed-strategy Nash equilibrium of game G:…”

Section: Mixed-strategy Equilibriamentioning

confidence: 99%

Cooperative Occupancy Decision Making of Multi-UAV in Beyond-Visual-Range Air Combat: A Game Theory Approach

Wang

et al. 2020

IEEE Access

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In this paper, a new cooperative occupancy decision-making problem for multiple unmanned aerial vehicles (UAVs) in beyond-visual-range (BVR) air combat is proposed; that is, UAV formation on each side first decides the occupancy positions of their own UAVs, then decides the target that each UAV will confront, so that each side can occupy the greatest predominance and be subject to the smallest threat possible. By analyzing the influence of the occupancy positions of the UAVs on the predominance gained by both sides and the threat against them, the problem is described as a zero-sum matrix game. Because the strategy combinations of this game are very numerous, as the best algorithm for the zero-sum matrix game, the Double Oracle (DO) algorithm still has difficulty solving the game model effectively. Therefore, we propose a DO combined with neighborhood search (DO-NS) algorithm to deal with the large-scale zero-sum matrix game. The results show that compared with the DO algorithm, the DONS algorithm can ensure the effectiveness of the computational time and solution quality. INDEX TERMS Multiple UAVs cooperative occupancy decision making, BVR air combat, zero-sum matrix game, multiple UAVs cooperative target assignment, double oracle algorithm.

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Section: Mixed-strategy Equilibriamentioning

confidence: 99%

Cooperative Occupancy Decision Making of Multi-UAV in Beyond-Visual-Range Air Combat: A Game Theory Approach

Wang

et al. 2020

IEEE Access

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“…Bu bölümde sıfır toplamlı oyunların çözümü için hem literatüre İzgi ve Özkaya [9,11] aşağıdaki gibi sıfır toplamlı iki kişilik bir oyunun getiri matrisi olsun.…”

Section: öRneklerunclassified

“…İzgi ve Özkaya literatürde ilk olarak matris normları ile oyun teorisini 2018 yılında yayınladıkları makale ile bir araya getirdiler [9]. Yaptıkları bu çalışmada iki kişilik sıfır toplamlı matris oyunlarının hem çözümüne hem de bu tür oyunların kurulumuna yönelik getiri matrisinin yalnızca 1-normunu ve -normunu esas alan yeni bir yaklaşım sunulmuştur.…”

Section: Introductionunclassified

“…Aynı yıl Özkaya ise yüksek lisans tezinde oyun teorisinde matris normlarının rollerini detaylı bir şekilde incelemiştir [10]. Bunların yanı sıra, İzgi ve Özkaya [9]'da sunmuş oldukları bu yeni yöntemlerini sıfır toplamlı olmayan iki kişilik bimatris oyunları için geliştirerek ve literatürde bilinen ünlü örneklerle de bu yaklaşımlarını güçlendiren ayrı bir çalışmaya imza attılar [11].…”

Section: Introductionunclassified

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Matris Normları ile Bir Matris Oyununun Adilliğinin Gösterilmesi

İzgi

Özkaya

2019

International Journal of Advances in Engineering and Pure Sciences

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Bu çalışmada, matris oyunlarını çözmek ve bu tür oyunları kurmak için literatüre yeni kazandırılmış ve yalnızca getiri matrisinin matris normlarından oluşan bir yöntemi kullanarak herhangi bir matris oyununun adil bir oyun olup olmadığını belirlemeyi hedefledik. Bunu yapmak için Taş-Kağıt-Makas oyununun genişletilmiş bir versiyonu olan Taş-Kağıt-Makas-Kertenkele-Spock (Rock-Paper-Scissors-Lizard-Spock) oyununu ana örnek olarak kullandık. Öncelikle oyunun gerçek sonucunu görmek için ilgili oyunu literatürde bilenen yöntemleri kullanarak çözdük. Daha sonra, herhangi bir lineer sistem çözmeksizin, sadece getiri matrisinin 1 ve normlarını kullanarak, bu oyunun adil bir oyun olup olmadığını detaylı bir şekilde farklı senaryolar altında yeni yöntemi kullanarak inceledik. Bunların yanı sıra, kare getiri matrisine sahip oyunların adil olup olmadığı çok daha hızlı bir şekilde gösterecek, getiri matrisinin determinantını içeren yeni bir teorem sunduk ve ispatladık. Son olarak sunduğumuz yeni teoremin uygulamalarını Taş-Kağıt-Makas-Kertenkele-Spock ve örnek olarak ele aldığımız diğer matris oyunları için de yaparak hızlı bir şekilde sonuçların elde edilebileceğini gösterdik.

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“…Moldalieva and Heathershaw demonstrated the role of the elite in the struggle for transparency and accountability in Kyrgyzstan’s mining sector in their study in 2020 and included game theory in their work [22] . In the same year, Izgi and Özkaya demonstrated the necessity of agricultural insurance with the MN-approach, in [23] , used in game theory [24] . As can be seen from the above examples, the use of game theory has improved a lot since its first day.…”

Section: Introductionmentioning

confidence: 99%

Effects of the quarantine on the individuals’ risk of Covid-19 infection: Game theoretical approach

Özkaya

İzgi

2021

Alexandria Engineering Journal

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In 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.

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A new perspective to the solution and creation of zero sum matrix game with matrix norms

Cited by 7 publications

References 13 publications

Cooperative Occupancy Decision Making of Multi-UAV in Beyond-Visual-Range Air Combat: A Game Theory Approach

Cooperative Occupancy Decision Making of Multi-UAV in Beyond-Visual-Range Air Combat: A Game Theory Approach

Matris Normları ile Bir Matris Oyununun Adilliğinin Gösterilmesi

Effects of the quarantine on the individuals’ risk of Covid-19 infection: Game theoretical approach

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