Optimal worst-case pricing for a logit demand model with network effects

We consider optimal pricing problems for a product that experiences network effects. Given a price, the sales quantity of the product arises as an equilibrium, which may not be unique. In contrast to previous studies that take a best-case view when there are multiple equilibrium sales quantities, we maximize the seller's revenue assuming that the worst-case equilibrium quantity will arise in response to a chosen price. We compare the best- and worst-case solutions, and provide asymptotic analysis of revenues.