A Nash equilibrium is determined for licenses-on-demand import quotas where licenses are allocated on a prorated basis. Inefficiency is incurred because licenses are allocated to high-cost firms. The ability to overbid exacerbates the inefficiency due to proportionate reductions in licenses. Quota expansion causes high-cost firms to decrease their bids but reduces inefficiency. The entry of a new firm causes all incumbent firms to increase bids or bid the quota. Not penalizing firms for the non-use of licenses increases inefficiency. The inefficiency impacts of tariff reductions, license fees, limits per firm, and imperfect information are also addressed. Copyright 2006, Oxford University Press.