COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1527RR

ROBUST MONOPOLY PRICING

Dirk Bergemann and Karl Schlag

July 2005
Revised April 2007
This revision: September 2008

We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version, the seller faces model uncertainty and only knows that the true demand distribution is in the neighborhood of a given model distribution.

We characterize the optimal pricing policy under two distinct, but related, decision criteria with multiple priors: (i) maximin expected utility and (ii) minimax expected regret. The resulting optimal pricing policy under either criterion yields a robust policy to the model uncertainty.

While the classic monopoly policy and the maximin criterion yield a single deterministic price, minimax regret always prescribes a random pricing policy, or equivalently, a multi-item menu policy. Distinct implications of how a monopolist responds to an increase in uncertainty emerge under the two criteria.

Keywords: Monopoly, Optimal pricing, Robustness, Multiple priors, Regret

JEL Classification: C79, D82