Classical Game Theory underpins much of AI and multiagent research, but hybrid Human AI systems require a framework in which execution authority can alternate within a digital environment. We introduce NeoGame Theory, an extension of classical Game Theory for hybrid Human AI coalitions operating under Virtual Nature, the algorithmic analogue of classical (physical) Nature. The framework combines a lexicographic coalition utility with a delegation rule based on the Jensen-Shannon divergence between Human and AI policies. Two thresholds define agreement, contextual, and disagreement regions. In the contextual region, execution follows a scenario specific rule. Apart from the theory, in this paper we develop the first regime, Human arbitration, in which the AI learns by observation and frequency matching while the Human retains final execution authority. We establish the axiomatic basis of the framework and characterize a frequency convergence equilibrium, providing the foundation for later extensions and computational validation.