aspg-34-3865-1792226266 20261017083746 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Prospects for Applied Mathematics and Data Analysis PAMDA 2836-4449 2024 4 2 Takaaki Fujita Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan Mathematical structures can generally be extended into Hyperstructures and SuperHyperstructures by leveraging powerset and n-th iterated powerset constructions (cf.7, 17, 31). These frameworks are particularly effective for representing hierarchical systems across various conceptual domains. Game Theory is a mathematical discipline for analyzing strategic interactions among rational agents with conflicting or cooperative objectives and finite choices.5, 10, 26 HyperGame Theory extends this by modeling situations in which players possess misperceptions or differing beliefs about the game being played.23 These ideas can be further generalized into the concept of SuperHyperGames.15 This paper explores the mathematical properties and illustrative examples of both HyperGame Theory and SuperHyperGame Theory. We hope that this investigation contributes to future developments in the theory and application of game-theoretic frameworks. 2024 01 08 3865 https://creativecommons.org/licenses/by/4.0/ 10.54216/PAMDA.040201 https://americaspg.com/journal/34/article/3865 https://americaspg.com/storage/articles/manuscripts/01M1MVGWQHA3KBMZ3AB1P172EN.pdf