Game theory demonstrates how GPOs save providers money
by Curtis Rooney
What is the impact of GPOs on healthcare-product supply chains? Recently, researchers at Purdue University used “game theory” to answer this question1. Among the specific questions asked and answered:
- Do providers experience lower total purchasing costs with a GPO in the supply chain?
- Do contract administration fees (CAFs) mean higher total purchasing costs for providers?
Before providing answers, we will provide a little background about game theory. Then we will review all of the major results of the Purdue study. Finally, in the closing section, Curtis Rooney, president of HIGPA, interviews Professor Leroy B. Schwarz, the study’s senior co-author.
A primer on game theory
Game theory is a widely used technique in economics. The most well-known game theorist is Nobel Prize Laureate John Nash (whose life is the subject of the book and movie “A Beautiful Mind”). It is used to examine situations in which “players” have competing interests. For example, in the Purdue study, healthcare manufacturers want to maximize profits while healthcare providers want to minimize their total purchasing costs.
As a scientific technique, game theory is like a laboratory test designed to examine the effects of a medication. That is, the conditions in game theory are tightly controlled – even unrealistic – compared to what happens in the real world. For example, the Purdue study examines a scenario in which providers are seeking the lowest total purchase cost for a single product. And, instead of considering a world in which several GPOs compete for providers’ business, the Purdue study assumes only a single GPO.
It is important to keep these laboratory conditions in mind when interpreting the results of any game-theory study. In other words, ask if a result is a consequence of a clearly unrealistic assumption, or if something else – more realistic and powerful – is causing the results to be what they are. Indeed, by keeping the possibly unrealistic assumptions in mind, it is possible to make hypotheses about how the results might carry over to a more realistic scenario.
The game
The Purdue study examines a supply chain that has several providers (e.g., hospitals) with different purchasing requirements for a single product; a single manufacturer, whose goal is to set its price schedule to maximize its profit; a competitive source selling the product at a fixed price; and a single GPO. Each provider is free to purchase some or all of its goods on contract through the GPO, direct from the manufacturer, or from the competitive source. In making its decision, the provider’s goal is to minimize its total purchasing cost, that is, the cost of the product plus the provider’s own contracting cost.
The Purdue study assumes that the provider’s contracting cost is the same if it contracts directly with the manufacturer or with the competitive source, but is less if it contracts through the GPO. This savings in contracting cost is called the GPO’s “contracting efficiency.” The GPO charges a contract administration fee to the manufacturer on all on-contract sales and a membership fee to providers who choose to use its services.
Note that in the game, it is assumed that the manufacturer’s goal is to maximize its profit, while the provider’s goal is to minimize its cost. The Purdue study further assumes that the GPO is a profit ”maximizer,” in particular, that the GPO might charge members a higher price than offered by the manufacturer. Since it is well known that some GPOs operate on a not-for-profit basis and, more generally, that such “margin-gain” doesn’t occur at any GPO, this assumption deserves an explanation.
For years, GPO critics have accused GPOs of profit-making, regardless of what GPO goals might actually be. So, in constructing the game, the Purdue researchers assumed what the critics have alleged – that the GPO’s goals are to maximize its profit. This was in order to see how manufacturers and providers might be affected in this worst-case scenario.
The rules of the game
Every game has rules. In the Purdue game, there are two important rules. The first involves “perfect information.” This means that every player knows everything that every other player knows. So, for example, the manufacturer knows the goals of the providers and the GPO, the contracting cost of the providers, and the price being offered by the competitive source. In reality, of course, only some of these things are known to some players, but not to others.
The second important rule involves the sequence in which the players make their choices. In the Purdue game, before the game starts, the GPO has chosen the manufacturer and they have agreed on the contract administration fee. The manufacturer “moves” first by choosing its price schedule. Next, the GPO chooses its on-contract price. Finally, the providers independently decide on whether to purchase direct from the manufacturer, through the GPO, from the competitive source, or some combination thereof.
In the language of game theory, the manufacturer is the “leader” of the game; i.e., it initiates the game by announcing a discount schedule. The GPO chooses next; and, finally, the providers decide how much to buy from each source. Everything else being equal, this tilts the playing field in favor of the manufacturer.
If this were, in fact, a game, then the manufacturer would get to “go” again; followed by the GPO, etc., like a simple around-the-table negotiation, each player taking its turn until the end. In fact, since the manufacturer knows everything that every other player knows, the manufacturer is in a position to anticipate how the GPO and then the providers will “move” in response to every possible decision it might make. So, the manufacturer will make a single decision – the one that is best for it – and the GPO and providers will do the same. After this first round, the manufacturer could, in theory, “go” again, but, since it made the best possible decision for itself in the first round, if it were allowed to “go” again, the manufacturer would make the very same decision. This is called “equilibrium.”
In game theory, as in real life, things either reach an equilibrium, where every player is satisfied with its last choice; or things never reach an equilibrium. In real life, unless an equilibrium is reached, someone eventually gets tired or disgusted, walks away, and the process simply stops. Game theory is focused on those scenarios when an equilibrium is reached, and then in interpreting what the equilibrium results are.
Do GPOs reduce providers’ purchasing costs?
The Purdue study concludes, “The GPO will set its price to be equal to … the price that equalizes the total purchasing cost of the largest provider that (the GPO wants) to buy on contract …. Providers with smaller purchasing requirements will experience lower total purchasing costs in the presence of a GPO, but higher per-unit prices.” So, the study concludes that, overall, GPOs decrease providers’ total purchasing costs, and, in particular, those for small providers.
Curtis Rooney: But what about the higher per-unit prices? And, does your study conclude that large providers don’t experience any savings in total purchasing cost?
Professor Schwarz: Remember, the providers are motivated to minimize their total purchasing cost. This is like a consumer choosing to purchase an item either at a supermarket or at a Sam’s Club. Assume that Sam’s Club has a lower price for the item. Does the smart buyer buy at Sam’s Club? If the Sam’s Club is next door and the supermarket is across town, then, yes! But, what if Sam’s Club is across town and the supermarket is next door? Whom to buy from should depend, in the language of the Purdue study, on the consumer’s “total purchasing cost,” which includes the consumer’s “contracting cost,” in this example, the cost of gasoline, parking, and, of course, the consumer’s time, plus the cost of the item to be purchased.
Now, suppose that the owner of the local supermarket knows that the consumer’s total purchasing cost to buy at Sam’s Club is, say, $10 – $4 for the item and $6 in contracting cost. In order to attract the consumer to buy from his supermarket, all he has to do is to set his price so that the consumer’s total purchasing cost is equal to $10 or slightly less, say $9.99. So, if the consumer’s contracting cost to buy at the supermarket is $5 (e.g., less time and gasoline), then the supermarket will set its price to $4.99. The result? The consumer will choose to buy at the supermarket, and incur a total purchasing cost of $9.99, one penny less than Sam’s Club, at $10. However, the consumer may pay more per unit ($4.99) than he/she would at Sam’s Club ($4).
Roughly the same thing is going on in our study, which has a single GPO (supermarket). Incidentally, this result is consistent with one of the findings of the 2002 study by the U.S. Government Accountability Office, namely, that buying through a GPO does not guarantee the lowest unit price.
Rooney: Is your result about possibly higher unit prices a consequence of one of the simplifications of the model?
Schwarz: Yes, it probably is. To see why, let’s return to the consumer’s decision. Suppose, now, that there are several local supermarkets whose “contracting costs” for the consumer are all about the same. This is like adding GPOs to the Purdue game. Now there will be competition among the supermarkets, each of them wanting the business of the consumer and each willing to reduce its per-unit price to do so. The result: lower per unit prices for the consumer. So, I believe that adding GPOs to the Purdue game will yield lower per-unit prices for the providers.
Rooney: What about large providers? The quoted result is that one or more of them won’t experience any savings in total purchasing cost in buying through the GPO.
Schwarz: Another factor that the Purdue game ignores is that large providers are often part owners of the GPO, and, hence, will receive share-backs and distributions. Under these circumstances, large providers buying through the GPO will experience lower (net) per-unit costs and, hence, lower total purchasing cost.
Do contract administration fees cause prices to rise?
The Purdue study concludes, “In the two special cases examined, the total purchasing cost of the providers is not affected by the CAF [contract administration fee]. Computational experiments indicate that this behavior occurs in the general3 case as well.” Hence, the Purdue study concludes that CAFs have no effect on the total purchasing costs of any provider, large or small.
Rooney: Manufacturers claim that CAFs increase their cost of doing business and force them to increase prices to all providers, whether they buy on contract or not.
Schwarz: As one of the members of the study team, I initially believed the manufacturers’ claim. I don’t anymore, based on our results. CAFs are similar to sales commissions paid by sellers to businesses like Groupon and LivingSocial. Although each operates in a slightly different manner, both businesses organize a group of volunteer buyers to purchase some given product or service from a specific seller. The seller, say a home-furnishing store, agrees to lower its price to each of the buyers in exchange for getting the business of the group. And, the seller pays a 30-to-50 percent commission to Groupon or LivingSocial for setting up the deal.
Notice that no one is forcing any given seller to sell to the group or to pay a commission to the group purchasing organization. So, I wouldn’t be surprised if that home-furnishing store complained that it has to charge all its customers more because of the commission it “has to” pay to the group purchasing organization. Would you?
Rooney: So, what does your study suggest would happen if the “safe harbor” provision of the Social Security law were removed, and GPOs were not allowed to charge CAFs to manufacturers?
Schwarz: Our study doesn’t directly address that question. We do address a scenario in which there is no GPO, and in it, providers pay higher total purchasing costs.
What affects GPO profits?
According to the Purdue study, “In the special cases examined, we have demonstrated that GPO profit is nondecreasing in its CAF and nondecreasing in the GPO’s contracting efficiency. Indeed, for low values of these parameters, the GPO makes no profit. Computational tests display the same behavior for more general cases.”
First, this result says that the higher the CAF the GPO is able to charge the manufacturer, then the higher the “profit” of the GPO. For not-for-profit GPOs, this means either lower prices for members or higher distributed profits for its member-owners. It also says that the more efficient the GPO is at contracting for its members, the higher its “profit.” This is an incentive for either for-profit or not-for-profit GPOs to get better at contracting.
Rooney: Our member GPOs have been saying for years that they are better at contracting than any single provider could possibly be. Are you saying that the more efficient the GPO becomes at contracting, the better off its provider-members will be?
Schwarz: In a word, yes. Our results tell us that, everything else being equal, a GPO’s “profit” will increase the more efficiently it is able to contract for its members. Higher “profit” means that the GPO is in a position to offer lower prices to all its provider members or to share its “profits” with member-owners.
Profits divided
How are supply-chain profits divided between the manufacturer and the GPO, and how is this influenced by the power of the GPO? According to the Purdue study, “As displayed in all cases examined, the GPO’s share of supply-chain profits are nondecreasing in both its CAF and its contracting efficiency. The more powerful the GPO is in negotiating its CAF, and the more efficient it is, the higher its profit and its share of total supply-chain profit.”
This result says that if one fixes the total profit that is made by either the manufacturer or the GPO, then the higher the CAF and the more efficient the GPO is at contracting, the more of that total profit goes to the GPO. Naturally, this motivates the GPO to charge higher, not lower CAFs. Also, as above, it motivates GPOs to become more and more efficient at contracting for its members.
This result and the result that CAFs don’t affect providers’ total purchasing cost are worthwhile considering together. In brief, CAFs don’t affect providers’ total purchasing cost, but CAFs reduce manufacturer profit; and the higher the CAF, the lower the manufacturer’s profits. Among other things, this result explains why manufacturers would like to reduce or eliminate them.
Curtis Rooney is president of the Health Industry Group Purchasing Association, www.higpa.org.