Modal Logic for Games

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Yarmohammadi, Amir Reza | 2024

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 57620 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Ardeshir, Mohammad
Abstract:
Game theory is a branch of mathematics that has a history of logical modeling. So far, various models have been presented for games in extensive and normal forms, games with complete and incomplete information, and games with perfect and imperfect information. In game modeling, pure strategies are often formulated; only in a few articles have mixed strategies been modeled. In this thesis, after a brief review of the definitions, terms, and fundamentals of game theory in Chapter Two, we will analyze one of the most important articles on modeling mixed strategies in Chapter Three. Then, in Chapter Four, we introduce epistemic modeling of games, which, within the framework of epistemic logic, examines the knowledge and beliefs of the players—fundamental concepts in game theory. In both of these chapters, modal logic serves as the primary tool for logical modeling. Finally, in Chapter Five, taking a different approach, we set aside formal logic and review a logical-philosophical article that analyzes the epistemic assumptions of a game
Keywords:
Game Theory ; Modal Logic ; Epistemic Logic ; Game Logic