Prescription Drug Pricing and Game Theory
https://www.nytimes.com/reuters/2017/09/15/business/15reuters-usa-healthcare-drugpricing.html
Over the past couple years, prices on prescription drugs have increased dramatically. According to the article, the price of two heart medications have gone up 720% and 310% since 2015. The price of EpiPens was multiplied by 6 from 2008 to 2016. However, Maryland is introducing a new price – gouging law to try and prevent these steep increases.
The pricing of prescription medicine can be modeled as a game theory problem. There are two players, the buyers, and the sellers. The buyer has two strategies: they can either buy the medicine or not buy the medicine. The seller has a large variety of strategies where each strategy is the price they can charge for the medicine. The payoffs are dependent on the type of medicine. For this example, let’s consider that the medicine is very important, and the buyer will suffer severe pain or injury without. As a result, the payoff the buyer gets is either feeling better or worse. If they take the medicine, they get 5, but if they don’t take the medicine, they get -200. The buyer also has a negative payoff in the price they pay. The seller gets a positive payoff if the buyer buys the medicine, and 0 otherwise. The strategies are summarized in this table.
| Buyer buys the medicine | Buyer does not buy the medicine | |
| Seller sells medicine for $50 | 50, -45 | 0,-200 |
| Seller sells medicine for $100 | 100, -95 | 0, -200 |
| Seller sells medicine for $150 | 150, -145 | 0, -200 |
| Seller sells medicine for $200 | 200, -195 | 0, -200 |
As shown, there is a pure strategy a pure strategy Nash Equilibrium where the seller sells the medicine for $200 and the buyer buys the medicine. When the payoff for not taking the medicine is so low for the buyer, as in the case for something like heart medications, the buyer’s best strategy is to buy the medicine at an extremely high price. Additionally, it’s possible that the payoff for the buyer to be potential death for not taking the medicine. This means that the buyer will potentially pay an infinite amount of money to avoid the negative payoff of death. However, this scenario where people pay an extreme amount of money for medicine starts to lead to other large negative payoff down the line, like not having enough money to pay rent or buy food. While the best strategy for the buyer is to buy the medicine and for the seller to sell the medicine at a very high price, this model is not sustainable for the buyer.