Robust Cournot Competition Under Cost Risk and Moment Ambiguity: Equilibrium, Welfare, and Learning Dynamics

This paper studies a Cournot duopoly in which marginal costs are uncertain, and firms are cautious about both risk and ambiguity. The static model uses a rectangular moment ambiguity set: each firm considers a range of plausible means and variances for its cost shock and evaluates output with a worst-case mean–variance criterion. This formulation makes the inner robust problem explicit and avoids assuming that a single uncertain support must maximize the mean and the variance at the same time. The worst case is the upper admissible mean together with the upper admissible variance, provided that this moment pair is attainable. Closed-form Nash–belief quantities are obtained for asymmetric and symmetric firms. Relative to a certainty-equivalent benchmark with the same expected cost, risk aversion lowers output; an expansion of the ambiguity set lowers it further. Prices move in the opposite direction, while consumer surplus and expected total surplus fall when output is pushed farther below the efficient level. The dynamic part combines partial adjustment toward the robust best response with smoothed updating of pessimistic moment estimates. With settled beliefs, the quantity map is affine, and its exact stability threshold is available in closed form. Stronger variance penalties flatten the reaction functions and enlarge the admissible adjustment range, creating a transparent trade-off between static welfare and dynamic stability. New parameter-plane regions show how pessimistic mean costs change market structure and how the variance penalty and adjustment speed organize convergence regimes. A flip boundary exists only in an extended parameter range, whereas a Neimark–Sacker bifurcation cannot arise from the two-dimensional strategic-substitute block alone.