Brown–Robinson method for interval matrix games

Akyar, Emrah; Akyar, Handan; Düzce, Serkan Ali

doi:10.1007/s00500-011-0703-6

Cited by 10 publications

(2 citation statements)

References 12 publications

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“…Liu and Kao (2009) applied the duality theorem and the variable substitution method to obtain a linear programming model for finding the bounds of the interval matrix game value. Akyar et al (2011) discussed the Brown-Robinson method to find the equilibrium point of the interval matrix game. Li (2011) created a linear programming method for determining the value of interval-valued matrix games.…”

Section: Introductionmentioning

confidence: 99%

Existence of optimal strategies in a normalized interval matrix game and applications

AFREEN¹,

Bhurjee

Aziz

2022

Preprint

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Vagueness in the real-world problem performs a significant role in determining the existence of a feasible solution to the problem. This vagueness in the model may be handled by considering the parameters of the problem as a closed interval. In this competitive world, game models with uncertain payoffs can successfully handle conflicting real-world problems. Therefore, a two-player zero-sum game model in which payoffs vary in a range is considered. Then, the existence of saddle point (pure strategy) and dominance rules are discussed for the game model, and mixed strategy is defined in the case of non-existing saddle point. Thereafter, a methodology has been developed to discuss the existence of weak and control strategies in the interval game model. Furthermore, we obtain the optimal value of the game model as a deterministic number. Finally, the developed methodology is successfully implemented to solve real-world investment problems in the stock market and obtain the optimal strategy to achieve the maximum return.

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Section: Introductionmentioning

confidence: 99%

Existence of optimal strategies in a normalized interval matrix game and applications

AFREEN¹,

Bhurjee

Aziz

2022

Preprint

View full text Add to dashboard Cite

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“…The matrix game with uncertain payoffs has been studied by several authors in different directions in last few years (see Levin 1999;Collins and Hu 2008a, b;Liu and Kao 2009;Nayak and Pal 2009;Gao et al 2009;Hladik 2010;Akyar et al 2011;Li 2011Li , 2012Dutta and Gupta 2014). Akyar et al (2011) considered twoperson interval matrix game and obtained a mixed strategy using Brown-Robinson's method. Li (2011) solved zero-sum game with interval payoffs by solving two deterministic linear programming problems and obtain the bounds of optimal value of the game.…”

Section: Introductionmentioning

confidence: 99%