A Timeless Game: A Game-Theoretic Model of Mass-Geometry Relations

Abstract

We develop a minimal, timeless game-theoretic representation of the mass-geometry relation. An "Object" (mass) and "Space" (geometry) choose strategies in a static normal-form game; utilities encode stability as mutual consistency rather than dynamical payoffs. In a 2x2 toy model, the equilibria correspond to "light-flat" and "heavy-curved" configurations; a continuous variant clarifies when only trivial interior equilibria appear versus a continuum along a matching ray. Philosophically, the point is representational: a global description may be static while the experience of temporal flow for embedded observers arises from informational asymmetry, coarse-graining, and records. The framework separates time as parameter from relational constraint without committing to specific physical dynamics.