Drug pricing and game theory

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The “battle of the commercials” has been going on for some time now. The AARP wants Congress to step in against high prescription prices, especially for “old staples” like insulin. In response, a near-tears diabetic says on my TV that Medicare is going to take her drugs away if Congress limits drug prices (no surprise, the commercial sponsored by PhRMA, the “big pharma” lobbyist).

I will be pleasantly surprised if much of anything gets done here in the end, as PhRMA has some Democratic congress members in their back pocket, but my longstanding take has been that the setting of prescription drugs prices is much more about politics than accounting, even when the government has not been directly involved. MBAs will say that the pharmaceutical firms are optimizing their price to maximize returns to the shareholders. Consumers see themselves being ripped off. However, I see drug pricing as a classic case of what economists and mathematicians call “game theory” on top of what accountants term the “fixed-cost dilemma.”

And the short version of the outcome is that, even with some kind of government price intervention, most of you will likely not see a significant change in prescription prices at your end of the transaction. But some could, and those “some” are important people in my book.

The fixed cost dilemma

In a 2018 post I illustrated why a short ambulance ride is now commonly being billed at $2000 or more in many communities. For any product or service that has a very high fixed cost of production (e.g., the same no matter how many times a day the ambulance leaves the barn) and a very low unit cost, or marginal cost, there is literally no single “correct” price to put on any one sale. You need another measuring stick, and that stick is often “the political winds.”

Take this simple example of developing and manufacturing a new drug. Let’s assume that we are a pharmaceutical firm, and we have a great new drug in the final stages of development. Before we sell the first pill, we will have spent $10 million in development costs, but once we get into large-scale production, the variable cost will only be one dollar for each pill manufactured. The problem here is that we have no idea if this pill will be approved by the regulators, or accepted in the market at all, let alone know how many units it will sell over its life. In other words, our new drug might sell 10 million units, or it might sell none.

If we ignore for the moment any profit we want to make, the chart below shows what we will need to charge per pill just to recover our development and production costs, and before we show any accounting profit. Note how dependent the drug’s cost per unit sold is on our “prophetic ability” to forecast sales.

Cost per unit

Many new drugs commonly cost ten times that amount in fixed costs or more. You can change any of my assumptions up or down, but the fixed-cost “amortization” math only gets more dramatic in variation in many “real world” cases. There will always be a huge difference in the per-pill cost of delivery for a niche or unpopular drug versus a massive seller. Can you see now why somebody is paying TV advertising dollars to promote drugs for conditions you never heard of, and with a list of side effects as long as your arm, recited at high speed?

This also means that whatever price the company places on that drug is likely to be a crap shoot. The best minds in the pharmaceutical industry are rarely prophetic enough to guess accurately on eventual market sizes. Price too high and you may lose out to a competitor or get public backlash. Price too low and you could fail to recover your development costs.

Game theory and the “drug players”

This is where the “game theory” sets in. I first discussed game theory in 2018 in regards to risky “friend or foe” decisions such as the North Korean nuclear threat. First articulated by mathematician John von Neumann in the 1940s, game theory refers to any economic or political condition where there are one or more “players” whose multiple options for countermoves to your actions make the end of the transaction mostly unpredictable. Is North Korea bluffing in their bombast? Are WE bluffing? There are big consequences based on decisions that our side does not control. But we could make matters worse. And that is the high-stakes “game” we are forced to play. You can “Monday morning quarterback” a bad decision, but that will likely not help you with the next one (cough, cough, Afghanistan).

The same thing is happening in pharmaceutical pricing. Various “players” are exerting political and economic power in immediate response to your decisions, and if you try to price like an accountant, or even a classic marketer, you will likely lose (and I am an accountant by training). “Game theory” political chess moves make the “cost per unit” basis for setting a price, as illustrated in my chart above, much less relevant, and even then, mostly as a measure of downside risk if you “lose the game.” As soon as those development costs are out the door, they are “sunk costs” and have no further economic effect on the outcome.

Von Neumann’s first game theory discussions related to simple two-player games. This is not his example, but think “Rock-Paper-Scissors” here. Now add more players and more complex, high-stakes rules:

  • Competitors may come up with a comparable drug, or better drug than yours. They could underprice you, but they also want to maximize profits and recover costs. So, how will they price their offering? You have no control over their decision, but it greatly impacts your outcome.
  • Governments, especially the better-run European universal healthcare systems (which use more different approaches than most Americans realize), often step in to put price pressure on selected drugs and manufacturers. Indeed, the U.S is an outlier in this regard among the most developed nations. A common approach is the “most favored nation” approach, in which Country A says, “We demand the best price you give to other countries, otherwise we will not approve your drug.” How will you play that move?
  • Hospital and medical service plans (incorrectly called “healthcare insurers”) and affiliated prescription service plans may attempt to secure favored pricing of key drugs. [1] These plans tie favored hospitals, medical practices, pharmacy chains and drug manufacturers together into “networks,” theoretically to keep prices down. But more accurately these are “cartels” for maximizing profits everywhere in the network (even in the so-called “non-profits”). Who will you “play ball” with in pricing your drug, and what happens if they eject you from their cartel?
  • Medicare Part D prescription plans offered to seniors have had the effect of “tiering” drug prices around four or five different price points featured in their different plan offerings. Drug manufacturers have access to the same math as the plan providers. If they price their drug too high, a plan provider may kick their drug up to the next-higher tier, hurting sales and angering customers. However, there is also no great incentive to price too low. That would create “foregone revenue,” the money the manufacturer could have made at a higher price that would still keep them in the tier. Prices from different manufacturers and drugs, as a result, naturally tend toward similar “tier prices.” It is a form of price collusion that requires no overt conspiracy.
  • The emergence of GoodRx and its competitors illustrates the growing power of social media to cap drug prices without government intervention. By openly publicizing the current prices of popular drugs at each major chain, they pressure the chains to accept discount coupons that GoodRx offers online. You can assume that the chains, with the aid of the manufacturers, are “gaming” a discounted price here that winds up in the end similar to the after-discount prices that they and the manufacturers have already negotiated with the major medical plans. In return, GoodRx and its competitors reap a nice bundle of marketable social media information about you and your “private” health history. As with Facebook and other social media, you become the product here.

The stakes of these “drug war games” have grown ever higher. Pricing at each different segment of the drug supply chain has become incredibly complex. It is not just manufacturer-to-pharmacy-to-customer. Discounts and incentives disguise the “true price” everywhere along the value chain from manufacturer to distributor to drugstore chain to prescription plan, and even reaching back to the prescribing doctors. Opportunities abound for drug manufacturers to strategically “move the profit margin” into different parts of the supply chain for different drugs like chess pieces in this multidimensional game.

Besides greatly complicating the pricing among the major health plans and pharmacies, these “war games” shut out the most vulnerable consumers and the people dependent on drugs who are not at the center of this pricing war. We still need some kind of federal intervention here, if only to prevent normal folk from becoming the “collateral damage” of the war among the corporate players.

Will government price controls work?

My take is a wishy-washy “yes and no.” For many of the most popular medications, this pricing game has likely already brought the “nominal price” down near the international “most favored nations” price for many drugs, via that complex mesh of discounts throughout the value chain. And it is in that complex mesh of markups itself where the healthcare industry tends to make its money. Taming that beast is a hard task.

People without a decent healthcare coverage plan are the ones usually screwed here, paying “rack rate” for their medications, and these are almost always the same people who can least afford it. Basic social justice would say, then, that government has a role in protecting those most abused by excess corporate power. No country’s “universal” healthcare system is simple, but the U.S. has an excess number of “profit-sucking leeches” at multiple points in the chain that other countries have eliminated.

Seniors making a “bad bet” on their Part D prescription plan choice, or not opting in at all, also get the short end of the stick here. One prescription change can easily amount to over $1000 on a 90-day supply of a medication, simply because the retiree chose last year not to pay a few dollars more every month for a plan that includes that one drug which is in a higher “formulary tier.” This tiering of prices with dramatic price differentials between each level is either a feature or a bug in the Part D system, depending on your perspective. As one gets older and subject to increasing medical needs, trying to save a few bucks every month on a cheap Part D plan, by my math, too often proves to be a fool’s errand.

And just like what happens when you squeeze a pillow, some “price bulges” will escape these complex “game theory” constraints. Insulin prices seem to be the largest target of Congress here. Indeed, it is difficult to understand why insulin is not so far along on the technology curve that it is not among the “$4.00 generics” so common in, for instance, statin drugs.

My view, after spending a lot of years in another industry that tried hard (eventually unsuccessfully) to maintain premium pricing on select products, is that the primary task of some of these pharmaceutical company CEOs is to hold the line on selected high-margin products in their portfolios. When you lose the “war game” on one key product and it crashes in market price, you need to make that loss up somewhere. Without a comprehensive government plan, this could wind up more “Whack-a-mole” than overall price control.

In the end, I have no sympathy for “Big Pharma,” and I doubt the warnings of loss of investment in innovative products. Coca-Cola and Pepsi managed to profitably sell soda in the deepest years of communism in the USSR and China. McDonalds’ Big Macs sell at competitive prices in European countries where the counter worker gets both a living wage and healthcare. Don’t cry for the capitalist drug manufacturers.


  1. “Hospital and Medical Service Plans” is how the Securities and Exchange Commission classifies what are more commonly called “healthcare insurers” such as Aetna and the Blue Cross companies. Rather than classic risk-bearing insurance, however, their biggest business is creating cartel-like networks of providers, and then processing claims from money pools established and collected by “self-insured” companies, their direct customers, through payroll deductions. Your own employer likely takes on most of the “health insurance” risk themselves. There is also likely a residual insurance policy protecting against a massive hit to the employer’s cost-sharing pool, but a separate “re-insurance” company usually takes on that risk.

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