We characterize the Nash equilibrium in the Hotelling model in the presence of an import quota. The optimal quota is identified and shown to be invariant to the mode of competition. We also prove that in the presence of a quota maximal differentiation is not achieved at equilibrium.
Boccard, N., & Wauthy, X. (2003). Optimal quotas, price competition and products’ attributes. The Japanese Economic Review, 54(4), 395-408. https://doi.org/10.1111/1468-5876.t01-1-00066 (Original work published 2003)