Rethinking Strategic Perception: Foundations and Advancements in

HyperGame Theory and SuperHyperGame Theory

Takaaki Fujita1,∗

1Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan

Email: takaaki.fujita060@gmail.com

Abstract

Mathematical structures can generally be extended into Hyperstructures and SuperHyperstructures by leverag-

ing 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 dis-

cipline 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 misper-

ceptions 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.

Keywords: Game Theory; HyperGame Theory; SuperHyperGame Theory; Hyperstructure; Superhyperstruc-

ture