Solving Defender-Attacker Game with Multiple Decision Makers Using Expected-Value Model

Document Type : Research Articles

Authors

1 Department of Science and Technology Studies, AJA Command and Staff University, Tehran. Iran

2 Faculty of Mathematical Sciences and Statistics, University of Birjand, Birjand. Iran

Abstract

Defender-attacker game is a model for conflicting between a defender and an attacker. Defender tries to prevent attacking an opponent by assigning limited security resources. In real world the utility values of the defender-attacker game are assigned by experts which usually are uncertain. According to that the assigned values by several experts may be slightly different and conflicting, we consider a set of all their viewpoints. This approach is similar to hesitant fuzzy environment. Also, each of the experts may have the different weights; AHP method is used to determine the weights of each of the experts. A weighted sum method is applied to obtain a game with aggregated payoffs. An expected value of the fuzzy numbers is introduced to convert the problem into defender-attacker game with interval payoffs. According to this, we proposed a method to solve security game in fuzzy environment. It is shown that the optimal solution of the expected value model is the optimal solution of the original model. Finally, a practical example is illustrated to solve by the proposed method.

Keywords

Caspian Journal of Mathematical Sciences (CJMS)
Volume 11, Issue 2
December 2022
Pages 368-380

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