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We study how to regulate a monopolistic firm using a robust-design, non-
Bayesian approach. We derive a 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 caps the firm’s average revenue. When his payoff is the total surplus of both
consumers and the firm, he offers a piece-rate subsidy to the firm while capping
the total subsidy. For intermediate cases, the regulator combines these three pol-
icy instruments to balance three goals: protecting consumers’ surplus, mitigating
underproduction, and limiting potential overproduction.
