We study the regulation of a monopolistic firm using a non-Bayesian approach. We derive the policy that minimizes the regulator’s worst-case regret, where regret is the difference between the regulator’s complete-information payoff and his realized payoff. When the regulator’s payoff is consumers’ surplus, he imposes a price cap. When his payoff is the total surplus of both consumers and the firm, he offers a capped piece- rate subsidy. For intermediate cases, the regulator uses both a price cap and a capped piece-rate subsidy. The optimal policy balances three goals: giving more surplus to consumers, mitigating underproduction, and mitigating overproduction.
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