Abstract
Game theory deals with the decision-making of individuals in conflicting situations with known payoffs. However, these payoffs are imprecisely known, which means they have uncertainty due to vagueness in the data set of most real-world problems. Therefore, we consider a two-person zero-sum game model on a larger scale where the payoffs are imprecise and lie within a closed interval. We define the pure and mixed strategy as well as value for the game models. The proposed method computes the optimal range for the value of the game model using interval analysis. To derive some important results, we establish some lemmas that relate the value of interval game models to their payoffs and then prove some important theorems. Furthermore, we establish the min-max theorem for the most and least mixed strategies of the game model. Then, we obtain the bounds of optimal mixed strategies as well as the approximate value of the game model. The developed theories are verified and demonstrated through realistic two-person zero-sum game models with interval payoffs.
Recommended Citation
Afreen, Sana and Bhurjee, Ajay Kumar
(2024).
(SI13-07) Optimal Range for Value of Two-person Zero-sum Game Models with Uncertain Payoffs,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 19,
Iss.
4, Article 1.
Available at:
https://digitalcommons.pvamu.edu/aam/vol19/iss4/1