Heuristic solutions for interval-valued games

Document Type : Research Article

Authors

• R.K. Gupta ¹
• D. Khan ²

¹ Department of Commerce and Management, West Bengal State University, Barasat, W.B., India.

² Faculty, Department of Business Administration, Burdwan Raj College, Burdwan, W.B., India.

10.22067/ijnao.2021.71321.1048

Abstract

When we design the payoff matrix of a game on the basis of the available information, then rarely the information is free from impreciseness, and as a result, the payoffs of the payoff matrix have a certain amount of ambiguity associated with them. In this work, we have developed a heuristic technique to solve two persons m × n zero-sum games (m > 2, n > 2), with interval-valued payoffs and interval-valued objectives. Thus the game has been formulated by representing the impreciseness of the payoffs with interval numbers. To solve the game, a real coded genetic algorithm with interval fitness function, tournament selection, uniform crossover, and uniform mutation has been developed. Finally, our proposed technique hasbeen demonstrated with a few examples and sensitivity analyses with respect to the genetic algorithm parameters have been done graphically to study the stability of our algorithm.

Keywords

• Two persons zero sum game
• Interval-valued payoffs
• Genetic Algorithm
• Order relations

20.1001.1.24236977.2022.12.1.10.4

Main Subjects

• Control and Optimization

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