Numerical Approach for Stochastic Matrix Games with Chaos Number Transformations

Creative Commons License

Özkaya M., İzgi B.

Karadeniz Fen Bilimleri Dergisi, cilt.16, sa.4, ss.1592-1608, 2026 (TRDizin)

Özet

Real-life situations are often analyzed using dynamic models. Stochastic matrix games and chaos numbers provide a tool for incorporating probabilities into these dynamic problems. In this study, we investigate chaos numbers and their  integration to the solution process of stochastic matrix games. We begin by representing the fundamentals of chaos numbers and their role in modeling chaos and explore their application in matrix games. Next, we introduce the concept of matrix games with chaos numbers, stochastic matrix games, and explain how they can be transformed into different types of games, along with the related solution method, such as the matrix norm method. We aim is to present an integration of chaos numbers and matrix games with chaos numbers to stochastic matrix games. To achieve this, we propose four different transformations to transition between various types of games, such as from stochastic matrix games to simple chaos games, from simple chaos games to static matrix games, and so on. We present an algorithm to apply these transformations and solve a stochastic matrix game in this context. As a result, we present a numerical solution method based on the transformation of stochastic matrix games into games involving chaos numbers and implement a matrix norm-based approach, known as the matrix norm method.