SOLVING MATRIX GAME USING ROUGH INTERVAL PAYOFFS

Ghosh P., Bhaumik A., Weber G. W., Roy S. K.

Journal of Dynamics and Games, vol.11, no.4, pp.399-421, 2024 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 4
  • Publication Date: 2024
  • Doi Number: 10.3934/jdg.2024010
  • Journal Name: Journal of Dynamics and Games
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Compendex, MathSciNet, zbMATH
  • Page Numbers: pp.399-421
  • Keywords: decision making problem, equilibrium strategies, graphical and algebraic method, linear programming, rough interval, Two-person zero-sum game
  • Middle East Technical University Affiliated: Yes

Abstract

In this paper, we conduct an analysis of a matrix game using rough interval payoffs, which we refer to as the rough interval matrix game (RIMG). We employ three methods to address the problem at hand: linear programming, graphical method, and algebraic method. The proposed approach offers several key advantages over existing methods, which we highlight. We introduce algorithms associated with each of the three mentioned methods to obtain optimal solutions for the RIMG. To validate the effectiveness of our proposed techniques, we present two numerical examples and apply the methodologies to solve them. In conclusion, we summarize the findings of our study and discuss potential avenues for future research based on the insights provided in this paper.