We study the regulation of a monopolistic firm using a robust-design approach. We solve for the policy that minimizes the regulator's worst-case regret, where the regret is the difference between his complete-information payoff and his realized payoff. When the regulator's payoff is consumers' surplus, it is optimal to impose a price cap. The optimal cap balances the benefit from more surplus for consumers and the loss from underproduction. When his payoff is consumers' surplus plus the firm's profit, he offers a piece-rate subsidy in order to mitigate underproduction, but caps the total subsidy so as not to incentivize severe overproduction.
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