Strategic decision-making under incomplete information traditionally assumes precise probabilistic beliefs, yet real-world agents often face fundamental ambiguity about the distributions governing opponents' characteristics. This paper addresses the computational challenge of solving finite Bayesian games where players hold interval-based ambiguous beliefs about opponents' type distributions—a setting that captures Knightian uncertainty while preserving analytical tractability. We establish the existence of Robust Nash Equilibrium through Kakutani's fixed-point theorem, proving that the best-response correspondence satisfies the necessary conditions for fixed-point existence. Equivalence to classical Bayesian Nash Equilibrium is demonstrated when ambiguity vanishes, confirming theoretical consistency with the standard framework. The solution methodology exploits the polytopic structure of marginal ambiguity sets: vertex enumeration reduces infinite-dimensional worst-case optimization to finite evaluation over product vertices, while linear programming reformulation enables efficient best-response computation. A key contribution is the provision of computable ε-equilibrium certificates that guarantee solution quality bounds. Complexity analysis identifies player and type counts as primary scalability barriers through exponential and super-exponential vertex growth, respectively, while action space size affects only linear programming dimensionality. Empirical validation across coordination games, social dilemmas, and mechanism design settings confirms algorithmic correctness and reveals game-dependent behavioral responses to ambiguity: coordination equilibria exhibit increased hedging as players protect against worst-case beliefs, cooperation collapses in social dilemmas through equilibrium refinement, while dominant-strategy mechanisms remain invariant to ambiguity perturbations. The framework provides practitioners with rigorous computational tools for equilibrium analysis when distributional knowledge is fundamentally incomplete.
D. Mazumder (Thu,) studied this question.