Dynamic Addiction Games

A continuous time dynamic price and quantity game is analysed between the seller and the consumer of an addictive substance. Consumption dynamics are modelled using a Becker Murphy rational addiction model. Conditional on the buyer's consumption strategy, a monopoly seller manipulates the price to maximise current value profits. The seller sets a low price at first and then raises the price as the consumer becomes addicted. The consumer understands this, and consumes less than would a myopic agent.