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Expensive Antibiotics and Game Theory

https://www.wired.com/story/antibiotics-pharma-price-jump-is-testing-one-of-medicines-oldest-questions/

We all know that pharmacies have been raising the prices for their drugs to absurd amounts of money. However, unlike cancer drugs or epinephrine, antibiotics are typically cheap. Antibiotics also costs the same to manufacture as many other kinds of drugs, such as cancer drugs. Not only is it normally too cheap for an effective profit, antibiotics cannot be used indefinitely, since bacteria will eventually develop resistances to that antibiotic, and will be rendered useless for doctors to treat with. For these reasons, many manufactures are getting out of investing in antibiotics, but in the end the general public still needs antibiotics.

 

There is one obvious way to increase production for manufactures in antibiotics: raising their prices.  Of course, pharmacies have already been raising the prices on so many other drugs, that buyers would be outraged now that even more drugs are being priced higher. This is where game theory can come in to find out just what policy makers should do in order to successfully increase production of antibiotics.

 

In my game, I have three players. I will be focusing on one manufacturing company named Nostrum Laboratories, that has raised their price on an antibiotic drug called nitrofurantoin. Nostrum can choose to produce more antibiotics or not. The policy makers are those who can choose to allow raised prices or keep the same price on antibiotics, and the buyers who can decide to buy antibiotics from Nostrum or not buy Nostrum antibiotics.

 

Nostrum wants buyers to buy and policy makers to allow them to give higher prices, so I initially gave them 9’s for Up $ and Buy. Policy makers want Nostrum to make more antibiotics, and buyers to buy more as well, so I had 9’s for Make and Buy. Finally buyers want prices to stay the same and Nostrum to make antibiotics, so there were 9’s for Make and Stay Same.

Here comes the complicated part:

I started all other numbers at 5 and depending on the result, I gave a payoff for each player.

Nostrum likely wants higher prices more than more buyers to buy, so I made higher prices worth 2 points and buying worth 1 point, so whenever there wasn’t higher prices the payoff was 5-2= 3 for example. If there were higher prices and buyers were buying, then the payoff would be 5+2+1=8

Policy makers likely wants Nostrum to make more antibiotics more than having buyers to buy, so Make was worth 2 points, and buying 1 point.

Buyers likely wants prices to not go up more so than Nostrum making more antibiotics, so Stay Same was worth 2, and Make worth 1.

Finally, I subtracted for each player’s payoff for what would be worse for them if they made a certian decision. For example, policy makers would like it better if they didn’t have to give away as much money to Nostrum, so anywhere they had Up $, their payoff was subtracted by one. Buyers would rather not want to avoid buying antibiotics, because Nostrum’s antibiotics are the most convienient for those who cannot swallow a pill, so anywhere there was a Don’t Buy, the payoff was subtracted by one. For Nostrum, it would be less dangerous to invest into antibiotics, so Made was subtracted by one.

As a result of all these calculations for payoffs, I got this game. The first set of numbers are for Nostrum, second set for Policy Makers, and third set for Buyers.

 

In a Nash Equilibrium, buyers would always buy, since their payoff is always going to be higher if they decide to pay for antibiotics. Next, the policy maker’s best move is to keep the same price, and finally Nostrum’s best move would be to not make any antibiotics. However, even though this is the best Nash Equilibrium, the best social welfare move is to instead have the Buyers buy, Policy Makers stay the same, and Nostrum to contiune making antibiotics. In both cases, neither is actually going to be effective in reality, and as the article above said, raising prices is probably not going to be the way to solve the need for more antibiotic manufacturing.

 

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