PBM Competition in Pharmaceutical Supply Chain: Formulary Design and Drug Pricing

In this paper, we model the competition among multiple Pharmacy Benefit Managers (PBMs) for the patronage of a client organization. Each PBM selects a list of prices to be charged to the client organization for each of the branded and generic drugs within a therapeutical class (price decision) and a formulary list that assigns branded drugs to preferred or non-preferred tiers (formulary decision). Drug manufacturers offer rebates to PBMs for drugs on preferred tier of formularies. The individuals participating in the client’s pharmacy benefit plan are the ones consuming the drugs and making purchasing decisions, while the client organization is paying the majority of drug cost. The choices of the individuals and the client organization are governed by different utility measures. For this complex drug distribution setting and for competing PBMs, we show the existence and uniqueness of a pure Nash equilibrium on aggregate price and formulary decisions. Moreover, the formulary list for each PBM is a dominant choice, in the sense that it is optimal irrespective of the choices made by the competing PBMs. We characterize each PBM’s optimal formulary and equilibrium price decisions, and discuss the impact of various model primitives on these decisions. As an application of our model, we use it to gain insights on the impact of mergers in the PBM industry for both PBMs and the client. Finally, we extend our base model to the more general setting of multiple client organizations, each with drugs from multiple therapeutical classes.