Solving N-players Continuous Differential Games under Neutrosophic Environment

Abstract

Uncertainty plays a crucial role in decision-making problems, particularly in game theory. Various forms of uncertainty have been explored in the literature, including fuzzy, soft, rough, and interval-based approaches. Game theory has been extensively studied under these uncertainty models, with researchers addressing vagueness, and imprecision from multiple perspectives. More recently, neutrosophic sets have emerged as an alternative framework for handling uncertainty. Neutrosophic numbers effectively incorporate indeterminacy in decision-making by considering factors such as intuition, assumptions, judgment, behavior, evaluation, and preferences of decision-makers. This paper presents a novel approach to solving a new class of n-player continuous differential games within a neutrosophic framework. In the proposed methodology, the neutrosophic n-player continuous games are redefined into two separate crisp problems: the lower problem and the upper problem. The study further establishes the necessary and sufficient conditions for determining equilibrium strategies in neutrosophic continuous differential games. To demonstrate its effectiveness and practical applicability, the proposed method is validated through a numerical example.