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This paper deals with a novel variation of the versatile stochastic duel game that incorporates an energy fuel constraint into a two-player duel game. The energy fuel not only measures the vitality of players but also determines the power of the shooting projectile. The game requires players to carefully balance their energy usage, while trying to outmaneuver their opponent. This unique theoretical framework for the stochastic game model provides a valuable method for understanding strategic behavior in competitive environments, particularly in decision-making scenarios with fluctuating processes. The proposed game provides players with the challenge of optimizing their energy fuel usage, while managing the risk of losing the game. This novel model has potential for implementation across diverse fields, as it allows for a versatile conception of energy fuel. These energy fuels may encompass conventional forms, such as natural gas, petroleum, and electrical power, and even financial budgets, human capital, and temporal resources. The unique rules and constraints of the game in this research are expected to contribute insights into the decision-making strategies and behaviors of players in a wide range of practical applications. This research primarily focuses on deriving compact closed-form solutions, utilizing transformation and flexible analysis techniques adapted to varying the concept of the energy fuel level. By presenting a comprehensive description of our novel analytical approach and its application to the proposed model, this study aims to elucidate the fundamental principles underlying the energy fuel constraint stochastic duel game model. |
