Universal Game Theory: A Subjective and Dynamical Framework

Universal Game Theory (UGT) provides a mathematically rigorous framework for strategic interaction under heterogeneous subjective world models.Each player observes the environment through a non-invertible projection that compresses or distorts information, producing subjective utilities and individualized optimization landscapes. This framework addresses a fundamental limitation of classical and Bayesian game theory: the assumption of a shared objective world. We introduce subjective potentials and show that players’ adjustments follow a gradient-flow dynamic (g-flow) whose limit points correspond to subjectively stable equilibria. Under mild regularity conditions, g-flow admits a Lyapunov structure and converges to local minima of each player's subjective potential. This formulation captures multi-stability, path dependence, and divergent internal reasoning even when observable behavior coincides. UGT subsumes Bayesian games as the special case where all projections coincide, establishing it as a strict generalization of classical equilibrium theory.