PBM competition in pharmaceutical supply chain: Formulary design and drug pricing

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 therapeutic class (price decision) and a formulary list that assigns branded drugs to preferred or nonpreferred 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, whereas 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 formulary and price decisions, which represent the welfare-adjusted cost and welfare-adjusted price of each PBM’s plan, respectively. We characterize each PBM’s optimal formulary and equilibrium price decisions and discuss the impact of various model primitives. We apply our model to gain insights on the impact of mergers in the PBM industry.