Epistemic Map Games (EMG): Strategic Interaction without a Shared Objective Game

This work introduces Epistemic Map Games (EMG), a minimal extension of finite normal-form games designed to model strategic interaction under epistemic misalignment. In an EMG, players do not optimize over a single, commonly shared payoff structure. Instead, each agent evaluates outcomes through an individual epistemic map that transforms objective payoffs into subjective evaluations. Strategic equilibrium is defined directly over these subjective games, without assuming common knowledge of payoffs, representations, or beliefs. The framework deliberately avoids probabilistic types, belief hierarchies, or Bayesian uncertainty. Epistemic distortion is modeled structurally, as a transformation of payoff space, rather than as incomplete information about an underlying true game. Classical Nash equilibrium is recovered as a special case when all epistemic maps coincide. For finite games, we prove the existence of equilibrium in mixed strategies. The existence result is standard; the conceptual contribution lies in shifting the object of strategic optimization from a shared game to agent-specific representations of it. EMG is intended as a foundational framework, not as a behavioral model or an applied theory. Toy examples are provided solely for structural illustration. Potential application domains include cybersecurity, adversarial AI, strategic deception, and multi-agent systems, where agents routinely act on distorted, incomplete, or adversarially manipulated internal representations of the environment.