Prospects for Applied Mathematics and Data Analysis PAMDA 2836-4449 10.54216/PAMDA https://www.americaspg.com/journals/show/3865 2022 2022 Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan Takaaki Takaaki 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 2024 01 14 10.54216/PAMDA.040201 https://www.americaspg.com/articleinfo/34/show/3865